ELECTRO-DYNAMIC  MACHINERY 


FOR  CONTINUOUS   CURRENTS 


BY 

EDWIN  J.  HOUSTON,  PH.  D.   (PRINCETON) 

AND 

A.   E.   KENNELLY,  Sc.   D. 


^N 

HE  \ 

UNIVERSITY; 

f^tMhltX*       ^*r 


NEW    YORK  t 

THE  W.   J.  JOHNSTON  COMPANY 

253  BROADWAY 
1896 


COPYRIGHT,  1896,  BY 
THE  W.  J.  JOHNSTON  COMPANY. 


PREFACE. 


ALTHOUGH  several  excellent  treatises  on  machinery  employed 
in  electro-dynamics  already  exist,  yet  the  authors  believe  that 
there  remains  a  demand  for  a  work  on  electro-dynamic  ma- 
chinery based  upon  a  treatment  differing  essentially  from  any 
that  has  perhaps  yet  appeared.  Nearly  all  preceding  treatises 
are  essentially  symbolic  in  their  mathematical  treatment  of 
the  quantities  which  are  invoJv-ed,  even  although  such  treat- 
ment is  associated  with  much  practical  information.  It  has 
been  the  object  of  the  authors  in  this  work  to  employ  only  the 
simplest  mathematical  treatment,  and  to  base  this  treatment, 
as  far  as  possible,  on  actual  observations,  taken  from  practice, 
and  illustrated  by  arithmetical  examples.  By  thus  bringing 
the  reader  into  intimate  association  with  the  nature  of  the 
quantities  involved,  it  is  believed  that  a  more  thorough  appre- 
ciation and  grasp  of  the  subject  can  be  obtained  than  would 
be  practicable  where  a  symbolic  treatment  from  a  purely 
algebraic  point  of  view  is  employed. 

In  accordance  with  these  principles,  the  authors  have  in- 
serted, wherever  practicable,  arithmetical  examples,  illustrat- 
ing formulas  as  they  arise. 

The  fundamental  principles  involved  in  the  construction  and 
use  of  dynamos  and  motors  have  been  considered,  rather  than 
the  details  of  construction  and  winding. 

The  notation  adopted  throughout  the  book  is  that  recom- 
mended by  the  Committee  on  Notation  of  the  Chamber  of 
Delegates  at  the  Chicago  International  Electric  Congress 
of  1893. 

ia 


iv  PREFACE. 

The  magnetic  units  of  the  C.  G.  S.  system,  as  provisionally 
adopted  by  the  American  Institute  of  Electrical  Engineers,  are 
employed  throughout  the  book. 

The  advantages  which  are  believed  to  accrue  to  the  concep- 
tion of  a  working  analogy  between  the  magnetic  and  voltaic 
circuits,  are  especially  developed,  for  which  purpose  the  con- 
ception of  reluctivity  and  reluctance  are  fully  availed  of. 


CONTENTS. 


CHAPTER  I. 

GENERAL  PRINCIPLES  OF   DYNAMOS. 

Definition  of  Electro-Dynamic  Machinery.  General  Laws  of  the  Genera- 
tion of  E.  M.  F.  in  Dynamos.  Electric  Capability.  Output.  Intake. 
Commercial  Efficiency.  Electrical  Efficiency.  Maximum  Output. 
Maximum  Efficiency.  Relation  between  Output  and  Efficiency,  .  I 

CHAPTER  II. 

STRUCTURAL   ELEMENTS  OF  DYNAMO-ELECTRIC   MACHINES. 

Armatures.  Field  Magnets.  Magnetic  Flux.  Commutator  Brushes. 
Constant-Potential  Machines.  Constant-Current  Machines.  Magneto. 
Electric  Machines.  Separately-Excited  Machines.  Self-Excited 
Machines.  Series-Wound  Machines.  Shunt- Wound  Machines. 
Compound- Wound  Machines.  Bipolar  Machines.  Multipolar  Ma- 
chines. Quadripolar,  Sextipolar,  Octopolar  and  Decipolar  Machines. 
Number  of  Poles  Required  for  Continuous  and  Alternating-Current 
Machines.  Consequent  Poles.  Ring  Armatures.  Drum  Armatures. 
Disc  Armatures.  Pole  Armatures.  Smooth-Core  Armatures.  Toothed- 
Core  Armatures.  Inductor  Dynamos.  Diphascrs.  Triphasers. 
Single  Field-Coil  Multipolar  Machines.  Commutatorless  Continuous- 
Current  Machines, 9 

CHAPTER  III. 

MAGNETIC   FLUX. 

Working  Theory  Outlined.  Magnetic  Fields.  Direction,  Intensity,  Dis- 
tribution. Uniformity,  Convergence,  Divergence.  Flux  Density. 
Tubes  of  Force.  Lines  of  Magnetic  Force.  The  Gauss.  Properties 
of  Magnetic  Flux.  M.  M.  F.  Ampere-Turn.  The  Gilbert.  Flux 
Paths,  .  .......  29 

CHAPTER  IV. 

NON-FERRIC  MAGNETIC  CIRCUITS. 

Reluctance.  The  Oersted.  Ohm's  Law  Applied  to  Magnetic  Circuits. 
Ferric,  Non-Ferric,  and  Aero-Ferric  Circuits.  Magnetizing  Force. 
Magnetic  Potential.  Laws  of  Non-Ferric  Circuits,  .  .  .  .48 

CHAPTER  V. 

FERRIC   MAGNETIC   CIRCUIT. 

Residual  Magnetism.  Permeability.  Theory  of  Magnetization  in  Iron. 
Prime  M.  M.  F.  Structural  M.  M.  F.  Counter  M.  M.  F.  Reluc- 
tivity. Laws  of  Reluctivity.  .  .  *.  .*  .  ;  .  55 


viii  CONTENTS. 

CHAPTER  VI. 

AERO-FERRIC  MAGNETIC   CIRCUITS. 

Magnetic  Stresses.     Laws  of  Magnetic  Attraction.     Leakage,    .         .        .68 

CHAPTER  VII. 

LAWS  OF  ELECTRO-DYNAMIC   INDUCTION. 

Fleming's  Hand  Rule.     Cutting  and  Enclosure  of  Magnetic  Flux,      .         .     74 
CHAPTER  VIII. 

ELECTRO-DYNAMIC  INDUCTION   IN  DYNAMO  ARMATURES. 

Curves  of  E.  M.  F.  Generated  in  Armature  Windings.     Idle-Wire,  .     90 

CHAPTER  IX. 

ELECTROMOTIVE  FORCE  INDUCED   BY   MAGNETO  GENERATORS,  IO3 

CHAPTER  X. 

POLE  ARMATURES,  IIO 

CHAPTER  XI. 

GRAMME-RING  ARMATURES. 

E.  M.  Fs.  Induced  in.  Effect  of  Magnetic  Dissymmetry.  Commuta- 
tor-Brushes. Effect  of  Dissymmetry  in  Winding.  Best  Cross- 
Section  of  Armature,  .  .  .  .  .  .  .  .  .117 

CHAPTER  XII. 

CALCULATION  OF  THE   WINDINGS  OF  A   GRAMME-RING  DYNAMO,         I2& 

CHAPTER  XIII. 

MULTIPOLAR  GRAMME-RING   DYNAMOS. 

Belt-Driven  versus  Direct-Driven  Generators.  Reasons  for  Employing 
Multipolar  Field  Magnets.  Multipolar  Armature  Connections.  Effect 
of  Dissymmetry  in  Magnetic  Circuits  of  Multipolar  Generators.  Com- 
putations for  Multipolar  Gramme-Ring  Generator,  ....  135 

CHAPTER  XIV. 

DRUM   ARMATURES. 

Smooth-Core   and  Toothed-Core  Armatures.     Armature  Windings.     Lap 

Windings.     Wave  Windings,       ..,«....  152 

CHAPTER  XV. 

ARMATURE  JOURNAL  BEARINGS. 

Frictional  Losses  of  Energy  in  Dynamos.  Sight-Feed  Oilers  and  Self- 
Oiling  Bearings,  ..........  159 


CONTENTS.  IX 

CHAPTER  XVI. 

EDDY   CURRENTS. 

Methods  of  Lamination  of  Core.    Transposition  of  Conductors,         .         .  164 
CHAPTER  XVII. 

MAGNETIC   HYSTERESIS. 

Nature  and  Laws  of  Hysteresis.     Hysteretic  Loss  of  Energy.     Table  of 

Hysteretic  Loss.     Hysteretic  Torque,          .        .   ,     .         .         .        .172 

CHAPTER  XVIII. 

ARMATURE   REACTION  AND   SPARKING  AT  COMMUTATORS. 

Diameter  of  Commutation.  E.  M.  F.  of  Self-induction.  Inductance  of 
Coils.  Cross- Magnetization.  Back-Magnetization.  Leading  and 
Following  Polar  Edges.  Lead  of  Brushes.  Distortion  of  Field.  Con- 
ditions Favoring  Sparking  at  Commutator.  Conditions  Favoring 
Sparkless  Commutation.  Methods  Adopted  for  Preventing  Sparking,  179 

CHAPTER  XIX. 

HEATING  OF  DYNAMOS. 

Losses  of  Energy  in  Magnetizing,  Eddies,  Hysteresis  and  Friction.     Safe 

Temperature  of  Armatures,          .         .         .         .         .        .        .         .  199 

CHAPTER  XX. 

REGULATION  OF  DYNAMOS. 

Series- Wound,  Shunt-Wound  and  Compound-Wound  Generators.  Over- 
compounding.  Characteristic  Curves  of  Machines.  Internal  and 
External  Characteristic.  Computation  of  Characteristics.  Field 
Rheostats.  Series- Wound  Machines  and  their  Regulation.  Open-Coil 
and  Closed-Coil  Armatures,  ,  , 206 

CHAPTER   XXL 

COMBINATIONS  OF  DYNAMOS  IN   SERIES  AND   PARALLEL. 

Generator  Units.  Series-Wound  Machines  Coupled  in  Series.  Shunt- 
Wound  Machines  Coupled  in  Parallel.  Equalizing  Bars.  Omnibus 
Bars, ...  .  220 

CHAPTER  XXII. 

DISC-ARMATURES   AND   SINGLE-FIELD  COIL  MACHINES,  228 

CHAPTER  XXIII. 

COMMUTATORLESS  CONTINUOUS-CURRENT   GENERATORS. 
Disc  and  Cylinder  Machines,      ....    ^ — : r"~"*-s!         '  2^ 


x  CONTENTS. 

CHAPTER  XXIV. 

ELECTRO-DYNAMIC   FORCE. 

Fleming's  Hand-Rule.     Ideal  Electro-dynamic  Motor,       ....  241 
CHAPTER  XXV. 

MOTOR  TORQUE. 

Torque  of  Single  Active  Turn.     Torque  of  Armature-Windings.     Torque 

of  Multipolar  Armatures.     Dynamo- Power, 251 

CHAPTER  XXVI. 

EFFICIENCY   OF  MOTORS. 

Commercial  Efficiency  in  Generators  and  Motors  Compared.     Slow-Speed 

versus  High-Speed  Motors.     Torque-per-pound  of  Weight,          .         .  268 

CHAPTER  XXVII. 

REGULATION  OF  MOTORS. 

Control  of  Speed  and  Torque  under  Various  Conditions.     Control  of  Series- 
Wound  Motors, 280 

CHAPTER  XXVIII. 

STARTING  AND   REVERSING  OF  MOTORS. 

Starting  Rheostats.     Starting  Coils.     Automatic  Switches.     Direction  of 

Rotation  in  Motors,    ..........  297 

CHAPTER  XXIX. 

METER-MOTORS. 

Conditions  under  which  Motors  may  act  as  Meters, 309 

CHAPTER  XXX. 

MOTOR   DYNAMOS. 

Construction  and  Operation  of  Motor-Dynamos,          •        •        •        .        •  318 


€ 
OF  THE 
EVERSITY    ' 


ELECTRO-DYNAMIC  MACHINERY 

FOR  CONTINUOUS  CURRENTS. 


CHAPTER  I. 

GENERAL    PRINCIPLES    OF    DYNAMOS. 

I.  By  electro-dynamic  machinery  is  meant  any  apparatus 
designed  for  the  production,  transference,  utilization  or 
measurement  of  energy  through  the  medium  of  electricity. 
Electro-dynamic  machinery  may,  therefore,  be  classified  under 
the  following  heads  : 

(i.)  Generators,  or  apparatus  for  converting  mechanical 
energy  into  electrical  energy. 

(2.)  Transmission  circuits,  or  apparatus  designed  to  receive, 
modify  and  transfer  the  electric  energy  from  the  generators  to 
the  receptive  devices. 

(3.)  Devices  for  the  reception  and  conversion  of  electric 
energy  into  some  other  desired  form  of  energy. 

(4.)  Devices  for  the  measurement  of  electric  energy. 

Under  generating  apparatus  are  included  all  forms  of  con- 
tinuous or  alternating-current  dynamos. 

Under  transmission  circuits  are  included  not  only  conduct- 
ing lines  or  circuits  in  their  various  forms,  but  also  the  means 
whereby  the  electric  pressure  may  be  varied  in  transit 
between  the  generating  and  the  receptive  devices.  This 
would,  therefore,  include  not  only  the  circuit  conductors 
proper,  but  also  various  types  of  transformers,  either  station- 
ary or  rotary. 

Under  receptive  devices  are  included  any  devices  for  con- 
verting electrical  energy  into  mechanical  energy.  Strictly 
speaking,  however,  it  is  but  fair  to  give  to  the  term  mechanical 
energy  a  wide  interpretation,  such  for  example,  as  would  per- 


2  ELECTRO-DYNAMIC  MACHINERY. 

mit  the  introduction  of  any  device  for  translating  electric 
energy  into  telephonic  or  telegraphic  vibrations. 

Under  devices  for  the  measurement  of  electric  energy  would 
be  included  all  electric  measuring  and  testing  apparatus. 

In  this  volume  the  principles  underlying  the  construction 
and  use  of  the  apparatus  employed  with  continuous-current 
machinery  will  be  considered,  rather  than  the  technique  in- 
volved in  their  application. 

2.  A  consideration  of  the  foregoing  classification  will  show 
that  in  all  cases  of  the  application  of  electro-dynamic  machin- 
ery, mechanical   energy  is   transformed,   by  various  devices, 
into  electric  energy,  and  utilized  by  various  electro-receptive 
devices  connected  with  the  generators  by  means  of  conducting 
lines.     The  electro-technical  problem,  involved  in  the  practi- 
cal application  of  electro-dynamic  machinery,  is,  therefore,  that 
of  economically  generating  a  current  and  transferring  it  to  the 
point  of  utilization  with  as  little  loss  in  transit  as  possible. 
The  engineering  problem  is  the  solution  of  the  electro-technical 
problem  with  the  least  expense. 

3.  A   dynamo-electric  generator   is  a   machine   in  which   con- 
ductors are  caused  to  cut  magnetic  flux-paths,  under  conditions 
in  which  an  expenditure  of  energy  is  required  to  maintain  the 
electric  current.     Under  these  conditions,  electromotive  forces 
are  generated  in  the  conductors. 

Since  the  object  of  the  electromotive  force  generated  in  the 
armature  is  the  production  of  a  current,  it  is  evident  that,  in 
order  to  obtain  a  powerful  current  strength,  either  the  electro- 
motive force  of  the  generator  must  be  great,  or  the  resistance 
of  the  circuit  small. 

Electromotive  sources  must  be  regarded  as  primarily  producing, 
not  electric  currents,  but  electromotive  forces.  Other  things 
being  equal,  that  type  of  dynamo  will  be  the  best  electrically, 
which  produces,  under  given  conditions  of  resistance,  speed, 
etc.,  the  highest  electromotive  force  (generally  contracted 
E.  M.  F.).  In  designing  a  dynamo,  therefore,  the  electromo- 
tive force  of  which  is  fixed  by  the  character  of  the  work  it  is 
required  to  perform,  the  problem  resolves  itself  into  obtaining 
a  machine  which  will  satisfactorily  perform  its  work  at  a  given 


GENERAL  PRINCIPLES  OF  DYNAMOS.  3 

efficiency,  and  without  overheating,  with,  however,  the  maxi- 
mum economy  of  construction  and  operation.  In  other  words, 
that  dynamo  will  be  the  best,  electrically,  which  for  a  given 
weight,  resistance  and  friction,  produces  the  greatest  electro- 
motive force. 

4.  There  are  various  ways  in  which  the  electromotive  force 
of  a  dynamo  may  be  increased;  viz., 

(i.)  By  increasing  the  speed  of  revolution. 

(2.)  By  increasing  the  magnetic  flux  through  the  machine. 

(3.)  By  increasing  the  number  of  turns  on  the  armature. 

The  increase  in  the  speed  of  revolution  is  limited  by  well- 
known  mechanical  considerations.  Such  increase  in  speed 
means  that  the  same  wire  is  brought  through  the  same  mag- 
netic flux  more  rapidly.  To  double  the  electromotive  force 
from  this  cause,  we  require  to  double  the  rate  of  rotation, 
which  would,  in  ordinary  cases,  carry  the  speed  far  beyond 
the  limits  of  safe  commercial  practice. 

Since  the  E.  M.  F.  produced  in  any  wire  is  proportional  to 
its  rate  of  cutting  magnetic  flux,  it  is  evident  that  in  order  to 
double  the  E.  M.  F.  .in  a  given  wire  or  conductor,  its  rate  of 
motion  through  the  flux  must  be  doubled.  This  can  be  done, 
either  by  doubling  the  rapidity  of  rotation  of  the  armature  ;  or, 
by  doubling  the  density  of  the  flux  through  which  it  cuts,  the 
rate  of  motion  of  tne  armature  remaining  the  same. 

Since  the  total  E.  M.  F.  in  any  circuit  is  the  sum  of  the 
separate  E.  M.  Fs.  contained  in  that  circuit,  if  a  number  of 
separate  wires,  each  of  which  is  the  seat  of  an  E.  M.  F.,  be 
connected  in  series,  the  total  E.  M.  F.  will  be  the  sum  of  the 
separate  E.  M.  Fs.  If,  therefore,  several  loops  of  wire  be 
moved  through  a  magnetic  field,  and  these  loops  be  con- 
nected in  series,  it  is  evident  that,  with  the  same  rotational 
speed  and  flux  density,  the  E.  M.  F.  generated  will  be  pro- 
portional to  the  number  of  turns. 

An  increase  in  E.  M.  F.  under  any  of  these  heads  is  limited 
by  the  conditions  which  arise  in  actual  practice.  As  we  have 
already  seen,  the  speed  is  limited  by  mechanical  considerations. 
An  increase  in  the  magnetic  flux  is  limited  by  the  magnetic 
permeability  of  the  iron — that  is,  its  capability  of  conducting 
magnetic  flux — and  the  increase  in  the  number  of  turns  is 


4  ELECTRO-DYNAMIC  MACHINERY. 

limited  by  the  space  on  the  armature  which  can  properly  be 
devoted  to  the  winding. 

5.  It  will  be  shown   subsequently  that   a   definite  relation 
exists   between   the   output  of  a   dynamo,    and    the   relative 
amounts  of  iron  and  copper  it  contains — that  is  to  say,  the 
type  of  machine  being  determined  upon,  given  dimensions  and 
weight  should  produce,  at  a   given  speed,  a  certain  output. 
The  conditions  under  which  these  relations  exist  will  form  the 
subject  of  future  consideration. 

6.  Generally  speaking,  in  the  case  of  every  machine,  there 
exists  a  constant  relation  between  its  electromotive  force  and 

E* 

resistance,  which  may  be  expressed  by  the  ratio,  — ,  where  £, 

is  the  E.  M.  F.  of  the  machine  at  its  brushes,  in  volts,  and  r, 
the  resistance  of  the  machine;  i.  <?.,  its  internal  resistance,  in 
ohms.  In  any  given  machine,  the  above  ratio  is  nearly  con- 
stant, no  matter  what  the  winding  of  the  machine  may  be; 
/.  e.y  no  matter  what  the  size  of  the  wire  employed.*  This 
ratio  may  be  taken  as  representing,  in  watts,  the  electric 
activity  of  the  machine  on  short  circuit,  and  may  be  con- 
veniently designated  the  electric  capability  of  the  machine. 
For  example,  in  a  200,  KW  (200,000  watts)  machine;  /.  *-.,  a 
dynamo,  whose  output  is  200  KW  (about  267  horse  power),  the 
value  of  the  electric  capability  would  be  about  10,000  KW, 

7Ta 

so  that,  since  — =  io,'ooo,ooo,  if  its  E.  M.  F.  were  155  volts, 

its  resistance  would  be  0.0024  ohm;  whereas,  if  its  E.  M.  F. 
were  100  volts,  its  resistance  would  be  approximately  o.ooi 
ohm. 

7.  Hitherto,  we  have  considered  the  energy  absorbed  by  the 
dynamo,    independently  of   its   external    circuit — that   is,   we 
have  considered  only  the  electric  capability  of  the  machine. 

When  the  dynamo  is  connected  with  an  external  circuit,  two 
extreme  cases  may  arise  ;  viz., 

*  This  ratio  would  be  constant  if  the  ratio  of  insulation  thickness  to  diameter 
of  wire  remained  constant  through  all  sizes  of  wire. 


GENERAL  PRINCIPLES  OF  DYNAMOS.  5 

(i.)  When  the  resistance  of  the  external  circuit  is  very 
small,  so  that  the  machine  is  practically  short  circuited.  Here 
all  the  electric  energy  is  liberated  within  the  machine. 

(2.)  When  the  external  resistance  is  so  high  that  the  resist- 
ance of  the  machine  is  negligible  in  comparison.  Here  practi- 
cally all  the  energy  in  the  circuit  appears  outside  the  machine. 
The  total  amount  of  work,  however,  performed  by  the  machine, 
under  these  circumstances,  would  be  indefinitely  small,  since 
the  current  strength  would  be  indefinitely  small.  Between 
these  two  extreme  cases,  an  infinite  number  of  intermediate 
cases  may  arise. 

8.  By  the  output  of  a  dynamo  is  meant  the  electric  activity 
of  the  machine  in  watts,  as  measured  at  its  terminals;  or,  in 
other  words,  the  output  is  all  the  available  electric  energy. 
Thus,  if  the  dynamo  yields  a  steady  current  strength  of  500 
amperes  at  a  steady  pressure  or  E.  M.  F.,  measured  at  its  termi- 
nals, of  no  volts,  its  output  will  be  no  X  500  =  55,000  watts, 
or  55  kilowatts. 

The  intake  of  a  dynamo  is  the  mechanical  activity  it  absorbs, 
measured  in  watts.  Thus,  if  the  dynamo  last  considered  were 
driven  by  a  belt,  which  ran  at  a  speed  of  1,500  feet-per-minute, 
or  25  feet-per-second,  and  the  tight  side  of  the  belt  exerted 
a  stress  or  pull  of  2,500  pounds  weight,  while  the  slack  side 
exerted  a  pull  of  710  pounds  weight,  the  effective  force,  or 
that  exerted  in  driving  the  machine,  would  be  1,790  pounds 
weight.  This  force,  moving  through  a  distance  of  25  feet 
per  second,  would  develop  an  activity  represented  by 
1,790  X  25=44,750  foot-pounds  per  second;  and  one  foot- 
pound per  second  is  usually  taken  as  1.355  watts,  so  that  the 
intake  of  the  machine  is  60,630  watts,  or  60.63  KW. 

By  the  commercial  efficiency  of  a  dynamo  is  meant  the  ratio  of 
its  output  to  its  intake.  In  the  case  just  considered,  the  com- 
mercial efficiency  of  the  machine  would  be  ,  ,  =  0.9072. 

60.63 

By  the  electric  efficiency  of  a  dynamo  is  meant  the  output, 
divided  by  the  total  electric  activity  in  the  armature  cir- 
cuit. Thus,  if  the  dynamo  just  considered  had  a  total  electric 
energy  in  its  circuit  of  57  KW,  of  which  2  KW  were  expended 

in  the,  machine,  its  electric   efficiency  would  be  —  =  0.965. 


6  ELECTRO-DYNAMIC  MACHINERY. 

9.  The  output  of  a  machine  would  be  greatest  when  the 
external  resistance  is  equal  to  the  resistance  of  the  machine. 
In  this  case,  the  output  would  be  just  one-quarter  the  electric 
capability,  and  the  electric  efficiency  would  be  0.5.  Thus, 
the  resistance  of  the  dynamo  considered  in  the  preceding  para- 
graph would  be,  say,  0.008  ohm,  and  the  electric  capability  of 

the  machine      Qg  =  1,512,500  watts,  or  1,512.5  KW.     If  the 

external  resistance  were  equal  to  the  internal  resistance— 
namely,  0.008  ohm,  the  total  activity  in  the  circuit  would  be 
756.25  KW;  the  output  would  be  378.12  KW,  and  the  electric 
efficiency  0.5. 

That  is  to  say,  in  order  to  obtain  a  maximum  output  from 
a  dynamo  machine,  the  circumstances  must  be  such  that  half 
the  electric  energy  is  developed  in  the  machine,  and  half  in  the 
external  circuit;  or,  in  other  words,  the  electric  efficiency 
can  be  only  0.5.  In  practice,  however,  it  would  be  impossible 
to  operate  a  machine  of  any  size  under  these  circumstances, 
since  the  amount  of  energy  dissipated  in  the  machine  would 
be  so  great  that  the  consequent  heating  effects  might 
destroy  it. 


10.  We  have  seen  that  whenever  the  resistance  in  the 
external  circuit  is  indefinitely  great,  as  compared  with  that 
of  the  machine,  the  electric  efficiency  of  the  machine  will  be 
i.o  or  100  per  cent.  It  is  evident,  therefore,  that  in  order  to 
increase  the  electric  efficiency  of  a  dynamo,  it  is  necessary 
that  the  resistance  of  the  external  circuit  be  made  great,  com- 
pared with  the  internal  resistance  of  the  machine.  For  ex- 
ample, if  the  external  resistance  be  made  nine  times  greater 
than  that  of  the  internal  circuit,  then  the  electric  efficiency 

will  be  -  -  =  0.9;  and,  similarly,  if  the  external  resistance 
be  nineteen  times  that  of  the  internal  resistance,  the  electric 

r 

efficiency  would  be  raised  to   -         -  =  0.95.     Generally  speak- 

ing, therefore,  a  high  electric  efficiency  requires  that  the 
internal  resistance  of  the  machine  be  small  as  compared  with 
the  external  resistance,  and,  also,  that  the  amount  of  power 


GENERAL  PRINCIPLES  OF  DYNAMOS.      .  7 

expended  in  local  circuits,  as  in  magnetizing  the  field  magnets 
of  the  dynamo,  be  relatively  small. 

11.  Care     must    be    taken    not   to    confound    the    electric 
efficiency     of     a    machine    with    its     electric     output.     The 
electric    output    of    a     machine    would     reach    a    maximum 
when    the    electric     efficiency     was     0.5     or    50    per    cent, 
and  the  output  would  be  zero   when   the    electric   efficiency 
reached    i.o. 

The  electric  efficiency  of  the  largest  dynamos  is  very  high, 
about  0.985.  Indeed,  the  electric  efficiency  of  large  machines 
must  necessarily  be  made  high,  since,  otherwise,  the  libera- 
tion of  energy  within  them  would  result  in  dangerous  over- 
heating. 

The  commercial  efficiency  of  a  dynamo  is  always  less  than 
its  electric  efficiency,  since  all  mechanical  and  magnetic 
frictions,  such  as  air  resistance,  journal-bearing  friction, 
hysteresis  and  eddy  currents  come  into  account  among  the 
losses.  The  commercial  efficiency  also  depends  upon  the  type 
of  machine,  whether  it  be  belt-driven,  or  directly  mounted  on 
the  engine  shaft,  since  the  mechanical  frictions  to  be  overcome 
differ  markedly  in  these  two  cases.  The  commercial  efficiency 
will  also  vary  with  the  character  of  the  iron  employed  in  its 
field  magnets  and  armature,  and  with  the  care  exercised  in 
securing  its  proper  lamination.  In  large  machines,  of  say 
500  KW  capacity,  the  commercial  efficiency  may  be  as  high 
as  0.95.  In  very  small  machines,  of  say  0.5  KW,  the  highest 
commercial  efficiency  may  be  only  0.6. 

12.  Although  in  the  United  States  it  is  the  practice  among 
constructors    generally,    to    calculate,  express   and    compare 
lengths  and  surface  areas  in  inches  and  square  inches,  when 
referring  to  dynamo  machinery,  and  although  it  might  seem 
therefore  more  suitable  to  adopt  inches  and  square  inches  as 
units  of  length  and  surface  throughout  this  book;  yet  the  fact 
that  the  entire  international  system  of  electro-magnetic  meas- 
urement is  based  on  the  centimetre,  renders  the  centimetre  and 
square  centimetre  the  natural  units  of  dimensions  in  electro- 
magnetism.     The   authors  have  therefore  preferred  to   base 


8  ELECTRO-DYNAMIC  MACHINERY. 

the  formulae  and  reasoning  in  this  volume  on  the  French 
fundamental  units,  in  order  to  simplify  the  treatment,  well 
knowing  that  once  the  elementary  principles  have  been 
grasped,  the  transition  to  English  measurements  is  easily 
effected  by  the  student.  The  following  data  will,  therefore,  be 
useful: 

i  inch  =      2.54  cms.  i  cm.  =  0.3937  inch. 

I  foot  =  30.48  cms.  I  cm.  =  0.03281  foot, 

i  sq.  inch  =  6.4515  sq.  cms.  I  sq.  cm.  =  0.155  sq.  in. 

I  cubic  inch  =  16.387  c.  c.  i  c.  c.  =  0.06102  c.  in. 


CHAPTER  II. 

STRUCTURAL    ELEMENTS    OF    DYNAMO-ELECTRIC    MACHINES. 

13.  Dynamo-electric  machines,   as    ordinarily  constructed, 
consist  essentially  of  the  following  parts;  namely, 

(i.)  Of  the  part  called  the  armature,  in  which  the  E.  M.  F. 
is  generated.  The  armature  is  generally  a  rotating  part, 
although  in  some  machines  the  armature  is  fixed,  and  either 
the  field  magnets,  or  the  magnetic  field,  revolve. 

(2.)  Of  the  part  in  which  the  magnetic  field  is  generated. 
This  part  is  called  \.\\t  field  magnet  and  provides  a  magnetic  flux 
through  which  the  conductors  of  the  armature  are  generally, 
actually,  and  always  relatively,  revolved. 

(3.)  Of  the  part  or  parts  that  are  employed  for  the  pur- 
pose of  collecting  and  rectifying  the  currents  produced  by  the 
E.  M.  F.  generated  in  the  armature;  /'.  ^.,  collecting  and 
commuting  them,  and  causing  them  to  flow  in  one  and  the  same 
direction  in  the  external  circuit.  This  portion  is  called  the 
commutator. 

(4.)  Bundles  of  wire,  metallic  plates,  metallic  gauze,  or 
plates  of  carbon,  pressed  against  the  commutator,  and  con- 
nected with  the  circuit  in  which  the  energy  of  the  machine  is 
utilized.  These  are  called  the  brushes. 

In  addition  to  the  above  parts,  which  are  directly  connected 
with  the  electric  actions  of  the  machine,  there  are  the  neces- 
sary mechanical  parts,  such  as  the  bearings,  shaft,  keys,  base, 
etc.,  which  also  require  attention. 

The  particular  arrangement  of  the  different  parts  will  neces- 
sarily depend  upon  the  type  of  machine,  as  well  as  on  the  char- 
acter of  the  circuit  which  the  machine  is  designed  to  supply. 

It  will,  therefore,  be  advisable  to  arrange  dynamo-electric 
machines  into  general  classes,  before  attempting  to  describe 
the  structure  and  peculiarities  of  their  various  parts. 

14.  Dynamos  may  be  conveniently  divided  into  the  follow- 
ing classes;  viz., 

/^  OF  THE 


10 


ELECTRO-D  YN'AM/C  MA  CHINER  Y. 


(i.)  Constant  potential  machines,  or  those  designed  to  main- 
tain at  their  terminals  a  practically  uniform  E.  M.  F.  under 
all  variations  of  load. 

To  this  class  belong  nearly  all  dynamos  for  supplying  incan- 
descent lamps  and  electric  railroads. 

Fig.  i  represents  a  particular  machine  of  the  constant- 
potential  type.  A,  A,  is  the  armature,  whose  shaft  revolves 
iti  the  self-oiling  bearings  B,  B.  C  is  the  commutator,  and  D, 
D,  are  triple  sets  of  brushes  pressing  their  tips  or  ends  upon 


FIG.   I. — CONTINUOUS-CURRENT   BIPOLAR   CONSTANT-POTENTIAL   GENERATOR. 


the  commutator.  F,  F,  are  the  field  magnets,  wound  with 
coils  of  insulated  wire.  T,  T,  are  the  machine  terminals,  con- 
nected with  the  brushes  and  with  the  external  circuit  or  load. 
The  whole  machine  rests  on  slides  with  screw  adjustment  for 
tightening  the  driving  belt. 

Constant-potential  generators  are  made  of  all  sizes,  and  of 
various  types. 

(2.)  Constant-current  machines,  or  those  designed  to  main- 
tain an  approximately  constant  current  under  all  variations  of 
load. 


STRUCTURAL   ELEMENTS. 


1 1 


Constant-current  machines  are  employed  almost  exclusively 
for  supplying  arc  lamps  in  series. 

Fig.  2  represents  a  form  of  constant-current  generator. 
This  is  an  arc-light  machine.  It  has  four  field  magnets  but 
only  two  poles,  Pl  and  P*,  connected  by  a  bridge  of  cast  iron 
at  B.  At  R,t  is  a  regulating  apparatus  for  automatically  main- 
taining the  constancy  of  the  current  strength,  by  rotating  the 


FIG.    2. — CONTINUOUS    CONSTANT-CURRENT   BIPOLAR    GENERATOR. 

brushes  back  or  forward  over  the  commutator,  under  the  influ- 
ence of  an  electromagnet  M. 

Constant-current  machines  are  made  for  as  many  as  200  arc 
lights;  /.  ^.,  about  10,000  volts  and  9  amperes,  or  an  output  up 
to  90  kilowatts  capacity,  but  such  large  sizes  are  exceptional. 

15.  Constant-potential  machines  may  be  subdivided  into 
sub-classes,  according  to  the  arrangement  for  supplying  their 
magnetic  flux — namely: 

(a.)  Jtfagneto-electric  machines,  in  which  permanent  magnets 
are  employed  for  the  fields. 

The  magneto-electric  generator  was  the  original  type  and 
progenitor  of  the  dynamo,  or  dynamo-electric  generator — but 


12  ELECTRO-DYNAMIC  MACHINERY. 

has  almost  entirely  disappeared.  It  is,  however,  still  used  in 
telephony,  the  hand  call  being  a  small  alternating-current  mag- 
neto generator,  driven  by  power  applied  at  a  handle.  The 
magneto-electric  generator  is  also  used  in  firing  mining  fuses, 
and  in  some  signaling  and  electro-therapeutic  apparatus. 

Fig.  3  represents  a  form  of  magneto-electric  generator. 
J/,  is  a  triple  group  of  permanent  magnets,  and  A,  is  the 
armature. 

(b.)  Separately-excited  machines,  in  which  the  field  electro- 
magnets are  excited  by  electric  current  from  a  separate  elec- 
tric source. 


FIG.    3. — ALTERNATING-CURRENT   MAGNETO-ELECTRIC   GENERATOR. 

A  particular  form  of  separately  excited  generator  is  repre- 
sented in  Fig.  4. 

Here  a  generator  A,  has  its  field  magnets  supplied  by  a 
small  generator  B,  employed  for  this  sole  purpose.  It  is  not 
necessary,  however,  that  the  exciting  machine  be  used  exclu- 
sively for  excitation.  Thus  two  generators,  each  employed  in 
supplying  a  load,  and  each  supplying  the  field  magnets  of  the 
other,  would  be  mutually  separately  excited. 

In  central  stations  large  continuous-current  machines  are 
occasionally,  and  alternating-current  machines  are  usually, 
separately  excited. 

(c.)  Self -excited  machines,  or  generators  whose  field  magnets 
are  supplied  by  currents  from  the  armature. 

Fig.  5  represents  a  form  of  self-excited  generator.  Mt  M, 
are  the  field  magnets,  />,  the  pilot  lamp;  i.  e.,  a  lamp  connected 
across  the  terminals  of  the  machine,  to  show  that  the  generator 
is  at  work.  S,  the  main  circuit  switch,  £,  the  rocker-arm 
carrying  the  brushes  B,  B. 


STRUCTURAL   ELEMENTS.  13 

16.  Self-excited  machines  maybe  divided  into  three  classes; 
viz., 

(i.)  Series  wound. 
(2.)  Shunt  wound. 
(3.)  Compound  wound. 

Series-wound  machines  have  their  field  magnets  connected 
in  series  with  their  armatures.     The  field  winding  consists  of 


FIG.    4. — ALTERNATING- CURRENT    MULTIPOLAR    SEPARATELY-EXCITED 
GENERATOR. 


stout  wire,  in  comparatively  few  turns.  Arc-light  machines 
are  almost  always  series  wound.  Fig.  6  represents  a  particular 
form  of  series-wound  machine  for  arc-light  circuits.  Here  the 
current  from  the  armature  passes  round  the  cylindrical  mag- 
nets M,  J/,  through  the  regulating  magnet  m,  and  thence  to 
the  external  circuit.  The  machine  in  Fig.  2  is  also  series 
wound. 

Shunt-wound  machines  have  their  field  magnets  connected 
to  the  main  terminals,  that  is,  placed  in  shunt  with  the  external 
circuit.  In  order  to  employ  only  a  small  fraction  of  .the  total 
current  from  the  armature  for  this  purpose,  the  resistance  of 
the  field  magnets  is  made  many  times  higher  than  the  resist- 


14  ELECTRO-DYNAMIC  MACHINERY. 

ance  of  the  external  circuit.  This  is  accomplished  by  winding- 
the  magnets  with  many  turns  of  fine  wire,  carefully  insulated. 

A  particular  form  of  shunt-wound  machine  is  represented  in 
Fig.  7. 

Here  the  fine  wire  windings  of  the  four  magnets  coils  are 
supplied  in  one  series  through  the  connecting  wires  W>  W,  WY 


FIG.    5. — SELF-EXCITED    CONTINUOUS-CURRENT    GENERATOR. 

from  the  main  terminals  of  the  machine,  one  of  which  is  shown 
at  M.  In  order  to  regulate  the  strength  of  the  exciting  cur- 
rent through  the  magnet  circuit,  it  is  usual  to  insert  a  hand- 
regulating  resistance  box,  called  the  field  regulating  boxy  in 
series  with  them. 

(d.)  Compound-wound  machines.  These  are  machines  that  are 
partly  shunt  wound  and  partly  series  wound. 

It  is  found  that  when  the  load  increases  on  a  series-wound 
generator,  it  tends  to  increase  the  pressure  at  its  terminals  ; 
i.e.,  to  raise  its  E.  M.  F.  On  the  other  hand,  when  the  load 
increases  on  a  shunt-wound  generator,  it  tends  to  diminish  the 
pressure  at  its  terminals;  i.  t.,  to  lower  its  E.  M.  F.  In  order, 
therefore,  to  obtain  good  automatic  regulation  of  pressure 


STRUCTURAL  ELEMENTS.  ,    15 

from  a  machine  under  all  loads,  these  two  tendencies'  are  so 
directed  as  to  cancel  each  other ;  this  is  accomplished  by 
employing  a  winding  that  is  partly  shunt  and  partly  series. 

Fig.  8  represents  a  particular  form  of  a  compound-wound 
machine. 

Here  there  are  two  spools  placed  side  by  side  on  each  mag- 
net-core, one  of  fine  wire  in  the  shunt  circuit,  carrying  a  cur- 
rent, and  exciting  the  fields,  even  when  no  current  is  supplied 
externally  by  the  machine,  and  the  other  of  stout  wire  making 


FIG.    6. — SELF-EXCITED    SERIES-WOUND   CONTINUOUS-CURRENT   GENERATOR. 

comparatively  few  turns.  This  is  part  of  the  series  winding 
which  carries  the  current  to  the  external  circuit.  The  excita- 
tion of  the  magnets  from  this  winding,  therefore,  depends 
upon  the  current  delivered  by  the  machine;  *'.  ^.,  upon  its 
load. 

Many  generators  for  incandescent  lamp  circuits,  as  well  as 
many  generators  for  power  circuits  are  compound  wound. 


17.  Besides  the  preceding  classes,  dynamo-electric  machines 
may  be  conveniently  divided  into  other  classes,  according  to 
a  variety  of  circumstances;  for  example,  they  may  be  divided 
according  to  the  number  of  magnetic  poles  in  the  field  frame, 
as  follows  : 


i6 


ELECTRO-D  Y NAM  1C  MA  CHINER  Y. 


(a)  Bipolar  machines,  or  machines  having  only  two  magnetic 
field  poles. 

Bipolar  machines  may  be  subdivided,  according  to  the  num- 
ber of  separate  magnetic  circuits  passing  through  the  exciting 


FIG.    7.— SELF-EXCITED   SHUNT-WOUND   CONTINUOUS-CURRENT   GENERATOR. 

coils,  into  single-circuit  bipolar,  double-circuit  bipolar  machines, 
and  so  on.  Generally,  however,  modern  bipolar  machines  are 
not  constructed  with  more  than  two  magnetic  circuits.  Figs, 
i,  2,  3  represent  bipolar  machines.  Of  these,  Fig.  i  possesses 
a  single  magnetic  circuit,  and  Fig.  2  a  double  magnetic  circuit. 

(b)  Multipolar  machines,  or  machines  having  more  than  two 
magnetic  poles. 

Fig.  9    represents  a  multipolar,  diphase  alternator  of  many 


STRUCTURAL   ELEMENTS.  17 

poles.     This  machine  was  employed  at  the  World's  Columbian 
Exhibition. 

18.  Multipolar  machines  may  be  divided  into  the  following 
sub-classes  : 

Quadripolar,  or  those  having  four  poles. 

Sextipolar,  or  those  having  six  poles. 

Octopolar,  or  those  having  eight  poles. 

Decipolar,  or  those  having  ten  poles. 

Beyond  the  number  of  ten  poles,  it  is  more  convenient  to 
omit  the  Latin  prefix,  and  to  characterise  the  machine  by  the 


FIG.    8. — COMPOUND-WOUND   CONTINUOUS-CURRENT   GENERATOR. 

number  of  poles,  as,  for  example,  a  i4-pole,  or  i6-pole  machine, 
etc. 

Quadripolar  machines  are  common.  Fig.  10  shows  a  quadri- 
polar  machine.  This  machine  has  four  brushes  and  is  com- 
pound wound.  It  is  designed  to  supply  from  500  to  600  volts 
pressure  at  its  brushes,  and  is  surmounted  by  a  group  of  six 
pilot  lights  in  series. 

Fig.  7  also  represents  a  quadripolar  generator. 

Fig.  ii  shows  a  form  of  continuous-current,  self-exciting, 
compound-wound,  sextipolar  machine,  arranged  for  direct  con- 
nection to  the  main  shaft  of  an  engine.  The  machine  is  pro- 
vided, as  shown,  with  six  collecting  brushes. 

Fig.  12  shows  an  alternating-current,  self-exciting,  octopolar 
generator  for  arc  circuits.  Although  this  machine  is  an  alter- 
nator ;  i.  e.,  supplies  alternating  currents,  it,  nevertheless, 


i8 


ELECTRO-D  YNA MIC  MA  CHINER  Y. 


supplies  its  field-magnet  coils  in  series  with  continuous  cur- 
rents from  the  commutator  C,  at  one  end  of  its  shaft.  The 
magnet  M,  forms  an  essential  part  of  a  short-circuiting  device, 
whereby  the  machine  is  automatically  short-circuited,  on  the 
external  circuit  becoming  accidentally  broken,  in  which  case 


FIG.    9.— ALTERNATING-CURRENT,    75O-KILOWATT   DIPHASE   MULTIPOLAR 
GENERATOR. 


the  pressure  generated  by  the  machine  might  become  so  great 
as  to  endanger  the  insulation  of  the  armature. 

Fig.  13  shows  a  decipolar  alternator,  separately  excited,  and 
compensating.  This  machine  is  belt-driven,  and  it  drives  in 
turn  a  small  dynamo  D,  employed  for  exciting  the  ten  field 
magnets.  The  commutator,  shown  at  C,  is  provided  for  the 
purpose  of  automatically  increasing  the  pressure  at  the  brushes 
of  the  machine  with  the  load,  so  as  to  compensate  for  drop  of 
pressure  in  the  line  or  armature.  In  other  words,  the  machine 
is  compound-wound. 


STRUCTURAL   ELEMENTS.  19 

As  we  have  already  observed,  bipolar  machines  may  be  sub- 
divided into  classes  according  to  the  number  of  magnetic 
circuits  passing  through  their  exciting  coils.  In  general, 
multipolar  machines  may  be  similarly  classified.  But,  as 
usually  constructed,  there  are  as  many  independent  magnetic 
circuits  as  there  are  poles.  Thus,  a  quadripolar  generator  has 


FIG.    IO. — CONTINUOUS-CURRENT    SELF-EXCITED    COMPOUND-WOUND 
QUADRIPOLAR    GENERATOR. 

usually  four  magnetic  circuits,  a  sextipolar  six,  and  so  on.  In 
some  cases,  however,  a  double  system  of  field  magnets  is  pro- 
vided, one  on  each  side  of  the  armature;  in  this  case,  the 
number  of  magnetic  circuits  may  be  double  the  number  of 
poles. 

Ip.   In   designing  a  continuous-current  generator,  the  num- 
ber of  poles  in  the  field  is,  to  a  certain  degree,  a  matter  of 


20  ELECTRO-DYNAMIC  MACHINERY. 

choice.  In  almost  all  cases,  directly-coupled,  continuous-cur- 
rent dynamos  are  multipolar,  while  belt-driven  dynamos  are 
frequently  bipolar.  Directly-coupled,  continuous-current  dy- 
namos are  usually  multipolar  machines,  owing  to  the  fact  that, 
in  order  to  conform  with  engine  construction,  they  have  to  be 
made  with  a  comparatively  slow  speed  of  rotation,  and,  since 


FIG.    II. — CONTINUOUS-CURRENT   SELF-EXCITED   GENERATOR. 

the  E.  M.  F.  generated  depends  upon  the  rate  of  cutting  mag- 
netic flux,  if  the  speed  of  the  conductor  is  decreased,  the  total 
amount  of  flux  must  be  correspondingly  increased.  This 
necessitates  a  greater  cross-section  of  iron  in  the  field  magnets 
in  order  to  carry  the  flux,  and  this  large  amount  of  iron  is  most 
conveniently  and  effectively  disposed  in  multiple  magnetic  cir- 
cuits. To  a  certain  extent  the  number  of  poles  is  arbitrary, 
but  usually,  in  the  United  States,  the  greater  the  output  of  a 
direct-driven  generator,  the  greater  the  number  of  poles. 

In  alternators,  however,  the  case  is  different.  Here,  in  order 
to  conform  with  a  given  system  of  distribution,  the  frequency 
of  alternation  in  the  current  is  fixed,  and,  since  the  speed  of 
revolution  of  the  armature  is  determined  within  certain  limits, 


STRUCTURAL   ELEMENTS.  21 


by  mechanical  considerations,  or  by  the  speed  of  the  driving" 
engine,  the  number  of  poles  is  not  open  to  choice,  but  is  fixed 
by  the  two  preceding  considerations.  In  any  alternator,  the 
number  of  alternations  of  E.  M.  F.  induced  per  revolution  in 
the  coils  of  its  revolving  armature,  is  equal  to  the  number  of 


M 


FIG.    12. — ALTERNATING-CURRENT    SELF-EXCITED    OCTOPOLAR    GENERATOR. 

poles.  Consequently,  an  alternator  producing  a  frequency  of 
X33~  5  tnat  is  a  frequency  of  133  complete  periods  or  cycles  per 
second,  delivers  266  alternations  from  each  coil,  and  its  arma- 
ture must,  therefore,  pass  266  poles  per  second. 

20.  Fig.  16  shows  a  i2-pole  alternator.     The  wires  a,  a,  are 
in  circuit  with  the  field  magnets,  and  serve  to  carry  the  current 
which  excites  them,  while  the  wires  b,  b,  lead  from  the  brushes. 

21.  Dynamo-electric  machines  may  also  be  divided,  accord- 
ing to  their  magnetic  circuits,  into  the  two  following  classes: 


22 


ELEC  TRO-D  YNA  MIC  MA  CHINER  Y. 


(a.)  Those  having  simple  magnetic  circuits  formed  by  a  single 
core  and  winding. 


FIG.    13. — ALTERNATING-CURRENT   SEPARATELY-EXCITED    DECIPOLAR 
COMPENSATING    GENERATOR. 


FIG.    14. — CONTINUOUS-CURRENT   CONSEQUENT-POLE   BIPOLAR    SHUNT- 
WOUND   GENERATOR. 

(b.)  Those  having  consequent  poles,  or  poles  formed  by  a 
double  winding;  that  is,  by  the  juxtaposition  of  two  poles  of 
the  same  name.  Dynamo-electric  machines  belonging  to  the 


Sl^RUCTURAL   ELEMENTS.  23 

first  class  are  shown  in  Figs,  i,  3  and  5.  A  type  of  machine 
belonging  to  the  consequent-pole  class  is  shown  in  Figs.  14  and 
15.  The  poles  are  shown  at^V,  N,  and  S,  S,  in  each  case,  the 
field  coils  being  so  wound  and  excited  as  to  produce  consequent 
poles. 


FIG.    15.— CONTINUOUS-CURRENT    CONSEQUENT-POLE    BIPOLAR   GENERATOR. 

22.  Dynamo  machines  may  also  be  classified  according  to 
the  shape  of  the  armature,  as  follows;  namely, 

(a.)  Ring  armatures. 

(b. )   Cylinder  or  drum  armatures. 

(c. )  Disc  armatures. 

(d. )  Radial  or  pole  armatures. 

(e. )  Smooth-core  armatures. 

(f. )   Toothed-core  armatures. 

Figs.  2  and  n  represent  examples  of  ring  armatures. 

Since  Gramme  was  the  first  to  introduce  the  ring  type  of 
armature,  this  form  is  frequently  called  a  Gramme-ring  armature. 

Figs,  i,  5  and  14,  show  examples  of  cylinder  or  drum  arma- 
tures. Disc  armatures  are  very  seldom  employed  in  the  United 
States.  An  example  of  a  disc  armature  is  shown  in  Fig.  19. 
An  example  of  a  radial  or  pole  armature  is  seen  in  Fig.  17. 


24  ELECTRO-DYNAMIC  MACHINERY. 

A  smooth-core  armature  is  one  on  which  the  wire  is  wound 
over  the  cylindrical  iron  core,  so  as  to  cover  the  armature  sur- 
face completely;  or,  if  the  wire  does  not  cover  the  surface  com- 
pletely, the  space  between  the  wires  may  either  be  left  vacant 
or  filled  with  some  non-magnetic  metal.  Such  armatures  are 
represented  in  Figs,  i,  2,  5,  15. 

A  toothed-core  armature,  on  the  other  hand,  is  one  on  which 


FIG.    16. — ALTERNATING-CURRENT   SEPARATELY-EXCITED    I2-POLE 
GENERATOR. 


the  wire  is  so  wound  in  grooves  or  depressions,  on  the  surface 
of  the  laminated  iron  core,  that  the  finished  armature  pre- 
sents an  ironclad  surface,  but  with  slots  containing  insulated 
copper  wire.  Such  an  armature  is  shown  in  Fig.  18  and 
also  in  Figs.  7,  10  and  n.  It  is  frequently  called  an  iron-clad 
armature. 


STRUCTURAL  ELEMENTS. 


25 


23.  Dynamos  may  also  be  divided,  according  to  the  actual 
or  relative  movement  of  armature  or  field,  into  the  following 
classes;  namely, 

(a.)  Those    in   which   the  field   is   fixed  and   the   armature 


^.          FIG.    17. — DIAGRAM   OF   POLE   ARMATURE. 

revolves.     This   class   includes  all   the    machines    previously 
described,  except  that  represented  in  Fig.  19. 

(b.)  Those   in  which    the   armature  is   fixed   and    the  field 
revolves.     An  example  of  this  type  of  machine  is   shown  in 


FIG.    l8. — A  TOOTHED-CORE   ARMATURE   SHOWING  THE    STAGES   OF 
WINDING. 


Fig.  19  A  and  B,  where  two  sets  of  field  magnets,  mounted  on 
a  common  shaft,  revolve  together  around  a  fixed  disc  arma- 
ture, shown  in  Fig.  19  B,  which  is  rigidly  supported  vertically 
in  the  space  between  them. 

(c.)  Those  in  which  the  field  and  armature  are  both  fixed, 
but  the  magnetic  connection  between  the  two  is  revolved. 
These  dynamos  are  usually  called  inductor  dynamos. 


26 


ELECTRO-D  YNAMIC  MACHINER  Y. 


24.  Dynamo  machines  may  also  be  divided,  according  to  the 
character  of  the  work  they  are  intended  to  perform,  into  the 
following  classes;  namely, 

(a.)  Arc-light  generators. 

(b. )  Incandescent-light  generators. 

(c. )  Plating  generators. 

(d.)   Generators  for  operating  motors. 


FIG. 


— ALTERNATING-CURRENT    DOUBLE    I2-POLE   GENERATOR    WITH 
FIXED    ARMATURE    AND    REVOLVING    FIELD    FRAMES. 


(e. )  Telegraphic  generators, 
(f. )  Therapeutic  generators. 
(g.)  Welding  generators. 

25.  Alternating-current  generators  may  be  divided,  accord- 
ing to  the  number  of  separate  alternating  currents  furnished 
by  the  machine,  into  the  following  classes;  namely, 

(a.)  Uniphase  alternators,  or  those  that  deliver  a  single  alter- 
nating current.  To  this  class  of  machines  belong  all  the 
ordinary  alternators  employed  for  electric  lighting  purposes. 

(b.)  Multiphase  alternators,  or  those  that  deliver  two  or  more 
alternating  currents  which  are  not  in  step. 


STRUCTURAL   ELEMENTS. 


27 


Some  multiphase  alternators  can  supply  both  single-pHase 
and  multiphase  currents  to  different  circuits. 

Multiphase  machines  may  be  further  subdivided  into  the 
following  classes;  namely, 

(i.)  Diphase  machines,  or  those  delivering  two  separate  alter- 
nating currents.  These  two  currents  are,  in  almost  all  cases, 


FIG.    IQB. — DISC    ARMATURE. 

quarter-phase  currents,  that  is  to  say,  they  are  separated  by  a 
quarter  of  a  complete  cycle.  Although  it  is  possible  to  employ 
any  other  difference  of  phase  between  two  currents,  yet  the 
quarter-phase  is  in  present  practice  nearly  always  employed. 

Fig.  9  represents  a  diphase  generator,  or  diphaser. 

(2.)  Triphase  machines,  or  triphasers,  are  generators  deliver- 
ing three  separate  alternating  currents.  These  three  currents 
are,  in  all  cases,  separated  by  one  third  of  a  complete  cycle. 

Uniphase  machines  are  sometimes  called  single-phase  machines, 
and  diphase  machines  are  sometimes  called  two-phase  machines 
or  tivo-phasers,  while  triphase  machines  are  sometimes  called 
three-phase  machines  or  three-phasers.  The  terminology  above 
employed,  however,  is  to  be  preferred. 

26.  In  addition  to  the  above  classification  there  are  the  fol- 
lowing outstanding  types  : 


28  ELECTRO-DYNAMIC  MACHINERY. 

(a.)  Single-field-coil  multipolar  machines,  or  machines  in  which 
multipolar  magnets  are  operated  by  a  single  exciting  field 
coil. 

(b.)  Commutatorless  continuous-current  machines,  or  so-called 
unipolar  machines,  in  which  the  E.  M.  Fs.  generated  in  the  arma- 
ture, being  obtained  by  the  continuous  cutting  of  flux  in  a 
uniform  field,  have  always  the  same  direction  in  the  circuit, 
and  do  not,  therefore,  need  commutation.  The  term  unipolar 
is  both  inaccurate  and  misleading,  as  a  single  magnetic  pole 
does  not  exist. 


CHAPTER  III. 

MAGNETIC    FLUX. 

27.  A  magnet  is   invariably  accompanied  by  an  activity  in 
the  space  or  region  surrounding  it.     Every  magnet  produces  a 
magnetic  field  or  flux,  which  not  only  passes  through  the  sub- 
stance of  the  magnet  itself,  but  also  pervades  the  space  sur- 
rounding it.     In  other  words,  the  property  ordinarily  called 
magnetism  is  in  reality  a  peculiar  activity  in  the  surrounding 
ether,  known  technically  3&*mctgiutic  flux. 

By  a  simple  convention  magnetic  flux  is  regarded  as  passing 
out  of  the  north-seeking  pole  of  a  magnet,  traversing  the  space 
"surrounding  the  magnet,  and  finally  re-entering  the  magnet  at 
its  south-seeking  pole.  Magnetic  flux,  or  magnetism,  is  cir- 
cuital; that  is,  the  flux  is  active  along  closed,  re-entrant  curves. 

28.  Although  we  are  ignorant  of  the  true  nature  of  magnetic 
flux,  yet,  perhaps,   the  most  satisfactory  working  conception 
we  can  form  concerning  it,  is  that  of  the  ether  in  translatory 
motion  ;  in  other  words,    in  a  magnet,   the  ether  is  actually 
streaming  out  from  the  north-seeking  pole  and  re-entering  at 
the  south-seeking  pole. 

Since  the  ether  is  assumed  to  possess  the  properties  of  a 
perfect  fluid  ;  /.  <?.,  to  be  incompressible,  readily  movable,  and 
almost  .infinitesimally  divisible,  it  is  evident  that  if  a  hollow 
tube,  or  bundle  of  hollow  tubes,  of  the  same  aggregate  dimen- 
sions as  a  magnet,  be  conceived  to  be  provided  internally  with 
a  force  pump  in  each  tube,  and  that  such  tube  be  placed  in  free 
ether,  then,  on  the  action  of  the  force  pumps,  a  streaming  would 
occur,  whereby  the  ether  would  escape  from  one  end  of  each 
of  the  tubes,  traverse  the  surrounding  space,  and  re-enter  at 
the  other  ends  of  the  tubes.  Moreover,  if  the  stream  lines, 
through  which  the  ether  particles  would  move  under  such  ideal 
circumstances,  were  mapped  out,  they  would  be  found  to  coin- 

29 


3°  ELECTRO-DYNAMIC  MACHINERY. 

cide  with  the  observed  paths  which  the  magnetic  stream  lines 
take  in  the  case  of  a  magnet. 

Similar  stream  lines  could  be  actually  observed  in  the  case 
of  a  hollow  tube  provided  internally  with  a  pump,  and  filled 
with  and  surrounded  by  water  ;  only,  in  this  case,  on  account 
of  the  friction  of  the  liquid  particles,  both  in  the  tube  and 
between  themselves,  work  would  require  to  be  done  and  energy 
expended  in  maintaining  the  motion,  and,  unless  such  energy 


FIGS.  2O  AND  20A. — DIAGRAMS  REPRESENTING  A  TUBE,  IMMERSED  IN  WATER , 
WITH  A  FORCE-PUMP  AT  ITS  CENTRE  AND  HYDROSTATIC  STREAM  LINES  — 
AND  A  CYLINDRICAL  BAR  OF  IRON,  MAGNETIZED,  I.  E.,  WITH  A  M.  M.  F. 
ACTIVE  WITHIN  IT  AND  MAGNETIC  FLUX  STREAM  LINES. 

were  supplied,  the  motion  would  soon  cease.  In  the  case  of 
the  ether,  however,  there  being,  by  hypothesis,  no  friction, 
although  energy  would  probably  be  required  to  set  up  the 
motion,  yet,  when  once  set  up,  no  energy  would  be  required 
to  sustain  it,  and  the  motion  should  coirtinue  indefinitely. 
This  is  similar  to  what  we  find  in  the  case  of  an  actual  steel 
magnet.  The  above  theory  is  merely  tentative.  The  real 
nature  of  magnetism  may  be  quite  different  ;  but,  for  practical 
purposes,  assuming  its  correctness,  since  there  is  no  knowledge 
as  to  the  pole  of  the  magnet  from  which  the  ether  issues,  it  is 
assumed,  as  above  stated,  to  issue  from  the  north-seeking  pole. 

29.  Fig.  20  represents,  diagramatically,  a  tube  provided  at 
its  centre  with  a  rotary  pump  Py  and  immersed  in  water.  If 
the  pump  were  driven  so  as  to  force  the  water  through  the  tube 


MAGNETIC  FLUX.  31 

in  the  direction  of  the  arrows;  i.  e.,  causing  the  water  to  enter 
the  tube  at  S,  and  leave  it  at  N,  then  stream  lines  would  be 
produced  in  the  surrounding  water,  taking  curved  paths,  some 
of  which  are  roughly  indicated  by  arrows. 

Fig.  20A  represents  the  application  of  this  hypothesis  to  the 
case  of  a  bar  magnet  of  the  same  dimensions  as  the  tube. 
Here  the  magneto-motive  force  of  the  magnet  corresponds  to  the 
water-motive  force  of  the  pump  in  Fig.  20,  and  is  hypothetically 
assumed  to  cause  an  ether  stream  to  pass  through  the  magnet 
in  the  direction  indicated  by  the  arrows  ;  namely,  to  enter  the 
magnet  at  the  south  pole  and  issue  at  the  north  pole.  These 
ether  streams  would  constitute  hypothetically  the  magnetic 


FIG.    21. — DISTRIBUTION   OF   FLUX   ABOUT   A   STRAIGHT   BAR   MAGNET  IN   A 
HORIZONTAL   PLANE,    AS   INDICATED   BY   IRON   FILINGS. 

flux,  and  would  pass  through  the  surrounding  space  in  paths 
roughly  indicated  by  the  arrows.  The  actual  flux  paths  that 
would  exist  in  the  case  of  a  uniformly  magnetized  short  bar 
magnet  are  more  nearly  shown  in  Fig.  21.  Here  it  will  be 
noticed  that  the  flux  by  no  means  issues  from  one  end  only  of 
the  magnet,  re-entering  at  the  other  end.  On  the  contrary, 
the  flux,  as  indicated  by  chains  of  iron  filings,  issues  from  the 
sides  as  well  as  from  the  ends  of  the  bar.  The  reason  for  this 
is  evidently  to  be  found  in  the  fact,  that  each  of  the  particles 
or  molecules  of  the  iron,  is,  in  all  probability,  a  separate  and 
independent  magnet,  and  therefore  must  issue  its  own  ether 
stream  independently  of  all  the  rest.  The  effect  is  therefore 
not  unlike  that  of  a  very  great  number  of  minute  voltaic  cells 
connected  in  series  into  a  single  battery,  and  the  whole 
immersed  in  a  conducting  liquid  where  side  leakage  can  exist. 


UNIVERSITY, 


32  ELECTRO-DYNAMIC  MACHINERY. 

30.  The  magnetic  field,  that  is  the  space  permeated  by  mag- 
netic flux,  may  be  mapped  out  in  the  case  of  any  plane  section 
by  the  use  of  iron  filings.  For  example,  Fig.  21,  before  alluded 
to,  as  representing  the  flux  of  a  straight-bar  magnet,  had  its 
flux  paths  mapped  out  as  follows  :  A  glass  plate,  covered  with 
a  thin  layer  of  wax,  was  rested  horizontally  on  a  bar  magnet, 
with  its  wax  surface  uppermost.  It  was  then  dusted  over  with 
iron  filings  and  gently  tapped,  when  the  iron  filings  arranged 
themselves  in  chain-forms,  which  are  approximately  those  of 


FIGS.    22,    A   AND   B. — MAGNETIC    FIELDS    BETWEEN   PARALLEL    BAR    MAGNETS. 

the  stream-lines  of  magnetic  flux.  A  satisfactory  distribution 
having  been  obtained  in  this  manner,  the  glass  plate  was  gently 
heated  in  order  to  fix  the  filings.  On  cooling,  the  filings  were 
sufficiently  adherent  to  the  plate  to  permit  it  to  be  used  as  the 
positive  from  which  a  good  negative  picture  can  be  readily 
obtained  by  photographic  printing. 

31.  A  modification  of  the  above  process  was  employed  in  the 
case  of  Figs.  22,  A  and  B,  shown  above.  Here  a  photographic 
positive  was  obtained  by  forming  the  field,  in  the  manner  pre- 
viously explained,  on  a  sensitized  glass  plate  in  a  dark  room, 
instead  of  on  a  waxed  plate  ;  and,  after  a  satisfactory  grouping 
of  filings  had  been  obtained  under  the  influence  of  the  field, 
exposing  the  plate  momentarily  to  the  action  of  light,  as,  for 


MAGNETIC  FLUX.  33 

example,  by  the  lighting  of  a  match.  The  filings  are  then 
removed,  the  plate  developed,  and  the  negative  so  obtained 
employed  for  printing. 

32.  Magnetic  flux  may  vary  in  three  ways;  namely, 

(i.)  In  direction. 

(2.)  In  intensity. 

(3.)  In  distribution. 

The  direction  of  magnetic  flux  at  any  point  can  be  readily 
determined  by  the  direction  assumed  at  that  point,  by  the 
magnetic  axis  of  a  very  small,  delicately  suspended  compass 
needle.  The  compass  needle  always  comes  to  rest  as  if  threaded 
by  the  flux,  which  enters  at  its  south  pole,  and  leaves  it  at  its 
north  pole,  thus  causing  the  needle  to  point  in  the  direction  of 
the  flux.  Assuming  that  a  compass  needle  may  be  represented 


FIG.    23. — HYDRAULIC   ANALOGUE   SHOWING  ATTRACTION  OF  OPPOSITE  POLES. 

by  a  little  tube  containing  an  ether  force  pump,  the  tube 
would  evidently  come  to  rest  when  the  flux  it  produced  passed 
through  it  in  the  same  direction  as  the  flux  into  which  it  was 
brought.  That  is  to  say,  if  the  needle  be  brought  into  the 
neighborhood  of  a  north  pole,  it  will  come  to  rest  with  its 
south  pole  pointing  toward  the  north  pole  of  the  controlling 
magnet,  since  in  this  way  only  could  a  maximum  free  ether 
motion  be  obtained.  If,  however,  the  compass  needle  be  held 
in  the  opposite  direction;  i.  e.,  with  its  north-seeking  pole 
toward  the  north-seeking  pole  of  the  magnet,  the  two  opposed 
stream  lines  will,  .by  their  reaction,  produce  a  repellent  force. 
These  effects  are  generally  expressed  as  follows  : 

Like  magnetic  poles  repel,  unlike  magnetic  poles  attract. 
Strictly  speaking,  this  statement  is  not  correct,  since,  what- 
ever theory  of  magnetism  be  adopted,  it  is  the  fluxes  and  not 
the  poles  which  exercise  attraction  or  repulsion. 

33-  Fig.  23  represents  the  action  of  the  flux  from  a  magnet 
upon  a  small  compass  needle,  as  illustrated  by  the  hydraulic 


34  ELECTRO-DYNAMIC  MACHINERY. 

analogy.  The  water  is  represented  as  streaming  through  the 
tube  O  Ny  and  issuing  at  the  end  N,  in  curved  stream  lines. 
Suppose  the  small  magnet,  or  compass  needle  6"  JV,  also  has  a 
stream  of  water  flowing  through  it,  entering  at  Sl9  and  leaving 
at  Nv.  Then,  if  the  compass  needle  be  free  to  move  about  its 
centre  of  figure,  it  will  come  to  rest  when  the  stream  from  the 
large  tube  O  TV,  flows  through  the  smaller  tube  from  S}  to  Nl 
that  is,  in  the  direction  of  its  own  stream. 

If,  however,  the  small  tube  Sl  N^  is  not  free  to  move,  but  is 
fixed  with  its  end  Nl  toward  the  end  N  of  the  larger  tube,  as 


FIG.    24. — HYDRAULIC    ANALOGUE    SHOWING   REPULSION   OF   SIMILAR   POLES. 

shown,  in  Fig.  24,  then  the  opposite  streams  will  conflict,  and 
produce,  by  their  reaction,  the  effect  of  repulsion  between  the 
tubes. 

34.  Magnetic  flux  possesses  not  only  definite  direction,  but 
also  magnitude  at  every  point;  that  is  to  say,  the  flux  is 
stronger  nearer  the  magnet  than  remote  from  it.  For  example, 
considering  a  magnet  as  being  represented  by  a  tube  with  an 
ether  force  pump,  the  velocity  of  the  ether  flux  will  be  a  maxi- 
mum inside  the  tube,  and  will  diminish  outside  the  tube  as  we 
recede  from  it.  The  intensity  of  magnetic  flux  is  generally 
called  its  magnetic  intensity  or  flux  density. 

Faraday,  who  first  illustrated  the  properties  of  a  magnetic 
field,  proposed  the  term  lines  of  magnetic  force,  and  this  term 
has  been  very  generally  employed.  The  term,  however,  is 
objectionable,  especially  when  an  attempt  is  made  to  conceive 
of  magnetism  as  possessing  flux  density,  or  as  varying  in 
intensity  at  any  point;  for,  in  accordance  with  Faraday's  con- 
ception, the  idea  of  an  increased  flux  would  mean  a  greater 
number  of  lines  of  magnetic  force  traversing  a  given  space. 
While  this  might  be  assumed  as  possible,  still  the  conception 
that  magnetism  acts  along  lines,  and  not  through  spaces,  is 
very  misleading.  An  endeavor  has  been  made  to  meet  this 


MAGNETIC  FLUX.  35 

objection  by  the  introduction  of  the  term  tubes  of  force.  A 
far  simpler  working  conception  is  that  of  velocity  of  ether. 
that  is,  increased  quantity  passing  per  second,  as  suggested 
by  the  force-pump  analogue.  Here  the  increased  flux  density 
at  any  point  would  simply  mean  an  increase  of  ether  velocity 
at  such  point. 

35.  Intensity  of  magnetic  flux   is  measured   in   the  United 
States,  in  units  called  gausses,  after  a  celebrated  German  mag- 
netician  named  Gauss.     A  gauss  is  an  intensity  of  one  line  of 
force,  or  unit  of  magnetic  flux,  per  square  centimetre  of  cross- 
sectional  area,  and  is  an  intensity  of  the  same  order  as  that 
produced  by  the  earth's  magnetism    on  its  surface.     For  ex- 
ample, the  intensity  of  the  earth's  flux  at  Washington  is  about 
0.6  gauss,  with  a  dip  or  inclination  of  approximately  70°. 

Magnetic  flux  may  be  uniform  or  irregular.  Fig.  25  A, 
shows  a  uniform  flux  distribution,  as  represented  diagrammati- 
cally,  by  straight  lines  at  uniform  distances  apart.  That  is  to 
say,  uniform  intensity  at  any  point  is  characterized  by  rectan- 
gularity  of  direction  in  path  at  that  point.  Irregular  intensity 
is  characterized  by  bending,  and  the  degree  of  departure,  from 
uniformity  is  measured  by  the  amount  of  the  bending.  Irreg- 
ular flux  density  may  be  either  converging,  as  at  B,  or  diverging, 
as  at  C.  Convergent  flux  increases  in  intensity  along  its  pathr 
and  divergent  flux  diminishes. 

36.  When  the  flux   paths  are  parallel  to   one  another,  the 
intensity  must  remain  uniform.     Thus,  in  Fig.  25  at  A,  let  the 
area,  A  BCD,  be  i  square  centimetre,  then  the  amount  of  flux 
which  passes  through  it  in  this  position,  or,  in   our   hydraulic 
analogue,  the  quantity  of  water  which  would  flow  through  it  in 
a  given  time,  will  be  the  same  if  the  area  be  shifted  along  the 
stream  line  parallel  to  itself  into  the  position  E  F  G  H. 

When  the  flux  converges,  as  at  B,  in  Fig.  25,  then  the 
amount  of  flux  passing  through  the  normal  square  centimetre 
/  J  K  L,  will,  further  on,  pass  through  a  smaller  intercepting 
area,  say  one-fourth  of  a  square  centimetre  M  N  O  P,  and 
consequently,  the  intensity  at  this  area  would  be  four  times 
greater,  and,  in  the  hydraulic  analogy,  the  same  quantity  of 
water  passing  per  second,  flowing  through  a  cross  sectional 


30  ELECTRO-DYNAMIC  MACHINERY. 

area  four  times  more  constricted,   will  flow  there  with  four 
times  the  velocity. 

When  the  flux  diverges,  as  at  C,  the  opposite  effect  is  pro- 
duced. Thus  the  flux  shown  in  the  figure  as  passing  through 
the  area  Q  R  S  T,  say  one-fourth  of  a  square  centimetre, 


Uniform  FLux 


Intensity  Unvarying 


B 


Convergent  Flux 


Intensity  Increasing 


Divergent  Flux  Intensity  Diminishing  ' 

FIG.    25. — VARIETIES   OF   FLUX. 

would,  at  U  V  W X,  pass  through  one  square  centrimetre,  at 
four  times  less  density,  or,  in  the  case  of  the  hydraulic  analogy, 
at  one-fourth  of  the  velocity. 

37.  The  existence  of  a  magnetic  flux  always  necessitates  the 
expenditure  of  energy  to  produce  it.  In  the  case  of  the  ether 
pump,  assuming  that  energy  is  required  to  establish  the  flow 
through  the  tube,  this  energy  being  imparted  to  the  ether, 
becomes  resident  in  its  motion,  so  that  ether,  plus  energy 
of  motion,  necessarily  possesses  different  properties  from  ether 


MAGNETIC  FLUX. 


37 


at  rest.  In  the  same  way  in  the  case  of  a  magnet,  the  energy 
required  to  set  up  the  magnetic  flux;  /.  e.,  to  magnetize  it,  is 
undoubtedly  associated  with  such  flux.  Wherever  the  mag- 
netic intensity  is  greatest,  there  the  corresponding  ether 
velocity,  according  to  our  working  hypothesis,  is  greatest,  and 
in  that  portion  of  space  the  energy  of  motion  is  greatest. 

38.  It  is  well  known,  dynamically,  as  a  property  of  motion, 
that  the  energy  of  such  motion  in  a  given  mass  varies  as  the 
square  of  the  velocity,  so  that,  by  analogy,  if  magnetic  flux 
density  corresponds  to  ether  velocity,  we  should  expect  that 
the  energy  associated  with  magnetic  flux  should  increase  with 


FIG.  26. — DISTRIBUTION   OF   FLUX   ROUND    A   VERTICAL   WIRE   CARRYING 
A   CURRENT,    AS   INDICATED   BY    IRON   FILINGS. 


the  square  of  its  intensity.  This  is  experimentally  found  to- 
be  the  case.  Thus  if  (B,  represents  the  intensity  of  magnetic 
flux,  expressed  in  gausses,  then  the  energy  in  every  cubic  cen- 
timetre of  space,  except  in  iron  or  other  magnetic  material; 

/n2 

i.  e.,  in  the  ether  permeated  by  such  intensity,   is  ^—  ergs. 

07t 

Thus,  if  a  cubic  inch  of  air  (a  volume  of  16.387   cubic  centi- 
metres), be  magnetized  to  the  intensity  of  3,000  gausses,  the 
energy  it  contains,  owing  to  its  magnetism,  will  be 
16.387  x  3,000  x  3,ooo 


8  x  3.1416 


=  0.5868  x  io7ergs.  =  0.5868  joule. 


39.  Just  as  in  the  electric  circuit, the  presence  of  an  electric 
current  necessitates  the  existence  of  an  E.  M.  F.  producing  it. 
so  in  a  magnetic  circuit,  the  presence  of  a  magnetic  flux  neces- 


3#  ELECTRO-DYNAMIC  MACHINERY, 

sitates  the  existence  of  a  magneto-motive  force  (M.  M.  F.) 
producing  it. 

We  know  of  but  two  methods  by  which  a  M.  M.  F.  can  be 
produced,  viz. : 

(i.)  By  the  passage  of  an  electric  current,  the  neighborhood 
of  which  is  invested  with  magnetic  properties;  /.  e.,  surrounded 
by  magnetic  flux; 

(2.)  As  a  property  inherent  in  the  ultimate  particles  of  cer- 


FIG.    27. — GEOMETRICAL   DISTRIBUTION   OF   FLUX   PATHS   ROUND    A   WIRE 
CARRYING   A   CURRENT. 


tain  kinds  of  matter,  possibly  the  molecules,  of  the  so-called 
magnetic  metals. 

The  passage  of  an  electric  current  through  a  long,  rectilin- 
ear conductor,  is  attended  by  the  production  of  a  magnetic 
field  in  the  space  surrounding  the  conductor.  The  distribution 
of  flux  in  this  field,  is  a  system  of  cylinders  concentric  to  the 
conductor,  and  is  directed  clock-wise  around  the  conductor,  if 
the  current  be  supposed  to  flow  through  the  clock  from  its  face 
to  its  back.  This  distribution  is  shown  in  Figs.  26,  27  and  28. 
Fig.  26  represents  the  distribution  as  obtained  by  iron  filings. 
The  density  of  the  flux  is  roughly  indicated  by  the  density  of 
the  corresponding  circles. 


MAGNETIC  FLUX.  39 

40.  Fig.  27  shows  the  geometrical  distribution  of  the  flux 
paths  around  a  wire  carrying  a  current,  which  is  supposed  to 
flow  from  the  observer  through  the  paper.  Here  a  few  of  the 
flux  paths  are  indicated  by  the  circles,  i,  2,  3,  4  and  5,  while 
the  direction  is  shown  by  the  arrows.  The  distribution  of  the 
flux  is  such  that  it  varies  in  intensity,  outside  the  wire,  inversely 
as  the  distance  from  the  axis  of  the  wire,  and  the  total  flux 
between  any  adjacent  pair  of  circles  in  the  figure  is  the  same, 


FLUX 


FIG.    28. — DIAGRAM    OF    RELATIVE    DIRECTIONS   OF   MAGNETIC   FLUX 
AND   ELECTRIC   CURRENT. 

for  example,  between  i  and  2,  or  between  4  and  5.  Or,  in  the 
hydraulic  analogue,  the  total  flow  of  water  per  second,  between 
any  pair  of  adjacent  circles  is  the  same,  as  between  the  circles 
2,  3,  or  4,  5,  the  velocity  diminishing  as  the  distance  from  the 
axis  of  the  wire. 

Fig.  28  represents  the  direction  of  the  flux  round  the  active 
conductor,  the  current  flowing  from  the  observer  through  the 
shaded  disc. 

» 

41.  The  physical  mechanism  of  the  magnetic  flux  produced 
by  a  current  is  unknown,  but  if  an  electric  current  be  assumed 
to  be  due  to  a  vortex  motion  of  ether  in  the  active  wire,  the 
direction  of  which  is  dependent  on  the  direction  of  the  current 
through  the  wire,  then  such  vortex  motion  will  be  accompanied 
by  such  a  distribution  of  circular  stream-lines  in  the  ether,  as  is 
actually  manifested,  and,  when  the  direction  of  the  current 
through  the  conductor  is  changed,  the  direction  of  the  stream- 
lines outside  the  conductor  will  also  necessarily  be  changed. 


4o 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


As  the  strength  of  the  current  through  the  wire  increases,  the 
velocity  of  the  ether  surrounding  the  wire  increases;  i.  e.,  the 
intensity  of  the  magnetic  field  everywhere  increases. 

42.  If  a  conductor  conveying  a  current  be  bent  in  the  form 
of  a  circle  as  shown  in  Fig.  29,  and  a  current,  of  say  one 
ampere,  be  sent  through  the  conductor,  there  passes  through 
the  loop  so  formed  a  certain  number  of  stream-lines  as  repre- 
sented diagrammatically.  If  now,  the  current  in  the  wire  be 


FIGS.    29   AND    30. — SINGLE   LOOP   OF   ACTIVE   CONDUCTOR,    THREADED 
WITH    FLUX,  AND   DOUBLE   LOOP   WITH    M.  M.  F.  DOUBLED. 

doubled,  that  is  increased  to  two  amperes,  the  flux  intensity 
everywhere  will  be  doubled.  The  same  effect,  however,  can 
be  practically  obtained  by  sending  one  ampere  through  the 
double  loop,  shown  in  Fig.  30,  provided  the  two  turns  lie  very 
close  together.  Magnetic  flux  through  a  loop,  will  depend, 
therefore,  upon  the  number  of  ampere-turns,  so  that,  by  wind- 
ing the  loop  in  a  coil  of  many  turns,  the  flux  produced  by 
a  single  ampere  through  the  coil  may  be  very  great.  The 
M.  M.  F.  produced  by  a  current,  therefore,  depends  upon  the 
number  of  ampere-turns. 

43.  The  unit  of  M.  M.  F.  may  be  taken  as  the  ampere-turn, 
and  it  frequently  is  so  taken  for  purposes  of  convenience.  The 
fundamental  unit,  however,  of  M.  M.  F.,  in  the  United  States, 
is  the  gilbert,  named  after  one  of  the  earliest  magneticians, 
Dr.  Gilbert,  of  Colchester.  The  gilbert  is  produced  by  —  of  a 

47T 


MAGNETIC  FLUX.  41 

C.  G.  S.  unit  current-turn,  and,  since  the  C.  G.  S.  unit  of  current 

is  ten  amperes,  the  gilbert  is  produced  by  —  ampere-turn   (0.8 

4  n 

approximately,   more  nearly   0.7958).      It   is    only  necessary, 
therefore,  to  divide  the  number  of  ampere-turns  in  any  coil  of 


•"         '*'       '''''' 


FIG  31. — DISTRIBUTION  OF   FLUX   IN   PLANE  OVER  A  HORSE-SHOE 
MAGNET. 

wire  by  0.8,  that  is  to  multiply  the  number  of  ampere-turns  by 
1.25,  more  nearly  1.257)  to  obtain  the  M.  M.  F.  of  that  coil 
expressed  in  gilberts. 

44.  Figs.  31  to  42  are  taken  from  actual  flux  distributions  as 
obtained  by  iron  filings,  and  represent  a  series  of  negatives  or 
positives  secured  by  the  means  already  described.  A  study  of 


FIG.    32. — DISTRIBUTION   OF   FLUX   IN    PLANE   OVER   A   HORSE-SHOE 
MAGNET. 

such  flux-paths  assists  the  student  to  mentally  picture  the  flux 
distributions  which  occur  in  practice. 

Figs.  31  and  32  are  the  respective  positive  and  negative 
photographic  prints  taken  in  the  case-  of  a  horse-shoe  magnet. 
Here  the  filings  are  absent  in  a  region  outside  the  magnet  in 
the  neighborhood  of  the  poles  N  S.  The  cause  of  this  is  as  fol- 
lows :  the  fields  were  obtained  by  sprinkling  iron  filings  over 


42  ELECTRO-DYNAMIC  MACHINERY. 

a  smooth  glass  surface;  the  tapping  of  the  surface  necessary 
to  insure  the  arrangement  of  the  filings  under  the  influence  of 
the  magnetic  flux,  has  caused  an  accumulation  of  filings 
around  these  poles  at  the  expense  of  the  gap  immediately  in 
front  of  the  poles  which  would  otherwise  be  more  fairly  filled. 


FIG.    33. — DISTRIBUTION    OF   FLUX   BY    IRON    FILINGS    IN    PLANE    OVER    POLES 
OF    ELECTRO-MAGNET. 


45.  The  student  should  carefully  avoid  being  misled  by  the 
supposition  that  the  relative  attractive  tendencies  of  the  iron 
filings  in  such  diagrams  represent  the  corresponding  densities 
of  the  magnetic  flux,  for  the  reason  that  in  a  uniform  mag- 
netic flux  such  as  shown  at  A,  in  Fig.  25,  there  is  no  attrac- 
tion of  iron  filings,  whatever  its  intensity,  although,  of  course, 


FIG.    34- — DISTRIBUTION    OF    FLUX    BY    CUT    IRON    WIRE    IN    PLANE 
OVER    POLES   OF    ELECTRO-MAGNET. 

a  directive  tendency  still  exists.  In  order  that  there  should 
be  any  attractive  tendency,  in  contradistinction  to  a  mere 
directive  tendency,  it  is  necessary  that  the  intensity  of 
the  magnetic  flux  shall  vary  from  point  to  point;  or,  in 
other  words,  that  the  flux  shall  be  convergent.  The  greater 
the  degree  of  convergence  the  greater  the  attractive  force. 
Consequently,  variations  of  flux  intensity  as  indicated  by  iron 


MAGNETIC  FLUX. 


43 


filings  always  exaggerate  the  appearance  of  flux  density. 
Generally  speaking,  it  is  only  the  directions  assumed  by  the 
filings  in  such  diagrams,  as  indicative  of  the  directions  of  the 
flux,  which  can  be  regarded  as  trustworthy.  The  neglect  of 
this  consideration  has  given  rise  to  a  popular  belief  that 
magnetic  streamings  occur  with  greater  density  at  points, 
than  at  plane  or  blunt  surfaces,  which  is  not  the  case.  There 
must  necessarily  be  a  rapid  convergence  or  divergence  of  mag- 


FIG.  .35.  —  PLAN   AND    SIDE   ELEVATION   OF    MAGNET   EMPLOYED 
IN    CONNECTION   WITH   FIGS.  36   AND   37. 

netic  flux  at  points,  although  the  maximum  density  may  not  be 
very  great.  Owing  to  this  convergence,  iron  filings,  particles, 
nails,  etc.,  are  attracted  more  powerfully  at  such  points,  even 
though  the  uniform  intensity  of  flux  at  plane  surfaces  in  the 
vicinity  may  be  greater. 


46.  Fig.  33  shows  the  distribution  of  magnetic  flux  as 
obtained  by  iron  filings  in  a  horizontal  plane  over  the  vertical 
poles  of  an  electro-magnet.  Here  the  flux-paths  pass  in 
straight  lines  between  the  nearest  points  of  the  adjacent  poles, 
and  in  curved  lines  over  all  other  parts  of  the  plane.  If  we 
imagine,  following  the  hydraulic  analogue,  that  water  streams 
proceed  from  minute  apertures  in  one  of  the  poles,  and  that 


44 


ELECT RO-D  Y NAM  1C  MA  CHINER  Y. 


the  magnet  is  immersed  in  water,  then  the  stream-lines  so  pro- 
duced in  the  water  as  it  emerges  from  pole  N,  and  enters 
through  pole  6',  will  be  the  same  as  is  indicated  by  the  iron 


FIG.  36. — DISTRIBUTION   OF   FLUX   BY    IRON    FILINGS    IN    PLANE   OVER   MAGNET 
SHOWN   IN    FIG.    35,  WITH    MAGNET    PRESENTED    VERTICALLY. 

filings.  Fig.  34  shows  a  similar  distribution  of  flux  over 
the  poles  of  the  same  electro-magnet,  where  short  pieces 
of  fine  soft  iron  wire  were  used  in  place  of  the  iron  filings. 


FIG.  37. — DISTRIBUTION   OF   FLUX   BY  IRON    FILINGS    IN   PLANE   OVER   MAGNET 
SHOWN   IN    FIG.   35,  WITH    MAGNET    PRESENTED    HORIZONTALLY. 

Here  the  flux-paths  have  practically  the  same  distribution  as  in 
the  preceding  case. 

Figs.  36  and  37  show  the  distribution  of  flux  by  iron  filings 
in  a  horizontal  plane  over  the  poles  of  the  magnet  represented 
in  Fig.  35,  the  magnet  being  presented  vertically  in  Fig.  36, 


MAGNETIC  FLUX 


45 


and  horizontally  in  Fig.  37,  to  the  plane.     Here  the  general 
distribution  of  flux  between  the  polar  surfaces  is  rectilinear. 


FIG.  38. — FLUX-PATHS   BETWEEN    DISSIMILAR   POLES. 

Fig.    38    illustrates    the    flux    distribution    attending    the 
approach  of  what  are  called  unlike  poles.     Here   the   ether 


FIG.  39. — FLUX-PATHS   BETWEEN   SIMILAR    POLES. 

streams  we  assume  to  issue  from  N,  in  entering  the  magnet  S, 
take  the  paths  indicated. 

Fig.    39    illustrates    the    flux    distribution    attending    the 


46  ELECTRO-DYNAMIC  MACHINERY. 

approach  of  what  are  called  like  poles.     Here  the  hypothetical 
ether  streams  issuing  from  N,  N,  impinge,  as  shown,  and  pro- 


FIG.  4O. — FLUX-PATHS   BETWEEN   TWO    PARALLEL   BAR    MAGNETS, 
SIMILAR   POLES   ADJACENT. 

duce  a  neutral  line,  A  A,  corresponding  to  slack  water  in  the 
hydraulic  analogue. 


FIG.    41. — FLUX-PATHS   BETWEEN   TWO    PARALLEL   BAR   MAGNETS 
OPPOSITE    POLES    ADJACENT. 

Fig.  40  shows  the  distribution   of1  flux   in  the  case  of  two- 
straight  bar  magnets  laid  side  by  side  with  like  poles  opposed. 


MAGNETIC  FLUX.  47 

The  imaginary  ether  streams  again  oppose   and  the  neutral 
line  B  B,  is  produced  as  shown. 

Fig.  41  shows  the  distribution  of  magnetic  flux  in  the  case 
of  two  straight  bar  magnets,  laid  side  by  side,  with  unlike 
poles  opposed.  Here,  according  to  hypothesis,  some  of  the 
ether  streams  issuing  from  each  magnet,  pass  back  through 
the  other  magnet,  the  remainder  closing  their  circuit  through 


FIG.    42. — FLUX-PATHS    SURROUNDING   ANOMALOUS   MAGNET. 

the  air  outside.  A  curious  central  region  between  the  mag- 
nets, bounded  by  curves  resembling  hyperbolas  is  shown  at 
C,  where,  by  symmetry,  no  ether  motion  penetrates,  and  thus 
corresponding,  in  the  hydraulic  analogue,  to  calm  water. 

Fig.  42  shows  the  distribution  of  flux  over  the  surface  of 
what  is  commonly  called  an  anomalous  magnet,  that  is  a  magnet 
having  two  similar  poles  united  at  its  centre;  or,  in  other 
words,  having  two  separate  magnetic  circuits.  Here  the  dis- 
tribution of  flux  is  similar  to  that  in  Fig.  40,  where  like  poles 
are  approached. 


CHAPTER  IV. 

NON-FERRIC    MAGNETIC    CIRCUITS. 

47.  As  we  have  already  seen,  magnetic  flux  always  flows  in 
closed  paths,  or  forms  what  is  called  a  magnetic  circuit.  The 
quantity  of  magnetic  flux  in  a  magnetic  circuit  depends  not 
only  upon  the  magneto-motive  force,  but  also  on  the  disposition 
and  nature  of  the  circuit.  For  example,  it  is  not  to  be  sup- 
posed that  the  flux  produced  by  the  12  ampere-turns  (15.084 
gilberts)  in  the  right-handed  coil  or  helix  of  Fig.  43,  by  one 
ampere  flowing  through  the  twelve  turns  shown,  would  be 


FIG.    43. — RIGHT-HANDED   HELIX   OF    12   TURNS   CARRYING   ONE   AMPERE. 

exactly  the  same,  either  in  magnitude  or  distribution,  as  the  flux 
from  a  single  turn  carrying  12  amperes,  although  the  M.  M.  F.  'KM; 
would  be  the  same  in  each  case.  Just  as  in  the  case  of  an 
electric  circuit,  the  current  produced  by  a  given  E.  M.  F. 
depends  on  the  resistance  of  the  circuit,  so  in  the  case  of  a 
magnetic  circuit,  the  magnetic  flux  produced  by  a  given  M. 
M.  F.  depends  on  a  property  of  the  circuit  called  its  magnetic 
reluctance,  or  simply  its  reluctance. 

Magnetic  reluctance,  therefore,  is  a  property  corresponding 
to  electric  resistance,  and  is  sometimes  denned  as  the  resist- 
ance of  a  circuit  to  magnetic  flux. 

The  resistance,  in  ohms,  of  any  uniform  wire  forming  portion 
of  an  electric  circuit  is  equal  to  the  resistivity,  or  specific  resist- 
ance, of  the  wire,  multiplied  by  the  length  of  the  wire,  and  divided 
by  its  cross-sectional  area.  In  the  same  way,  the  reluctance,  in 
oersteds,  of  any  uniform  portton  of  a  magnetic  circuit,  is  equal 
to  the  reluctivity,  Or  specific  magnetic  resistance  of  the  portion, 
multiplied  by  its  length  in  centimetres,  and  divided  by  its 
cross  sectional  area  in  square  centimetres.  The  reluctivity  of 

43 


NON-FERRIC  MAGNETIC  CIRCUITS.  49 


air,  wood,  copper,  glass,  and  practically  all  substances  except 
iron,  steel,  nickel  and  cobalt,  is  unity.  Strictly  speaking,  the 
reluctivity  of  the  ether  in  vacuous  space  is  unity,  but  the  dif- 
ference between  the  reluctivity  of  vacuum  and  of  all  non- 
magnetic materials  is,  for  all  practical  purposes,  negligibly 
small.  Thus,  the  reluctance  of  a  cylinder  of  air  space  of  10 
cms.  long  and  2  sq.  cms.  in  cross-sectional  area,  is  5  oersteds. 

48.  The  reluctance  of  a  circuit  is  measured  in  units  of  reluct- 
ance called  oersteds.  An  oersted  is  equal  to  the  reluctance  of 
a  cubic  centimetre  of  air  (or,  strictly  speaking,  of  air-pump 
vacuum)  measured  between  opposed  faces. 

Having  given  the  reluctance  of  a  magnetic  circuit,  and  its 
total  M.  M.  F.,  the  flux  in  the  circuit  is  determined  in  accord- 

s'' 
ance  with  Ohm's  law;  that  is  <£  =  —  where  <£,  is  the  flux  in 

ux 

webers,  SF,  is  the  magneto-motive  force  in  gilberts,  and  (R,  the 
reluctance  in  oersteds.  It  may  afford  assistance  to  con- 

trast  the  well-known  expression:  amperes  —    -r-  —  ,  with  the 

gilberts 


corresponding  magnetic  expression,  webers  = 


oersteds. 


49.  The  unit  of  magnetic  flux,  in  the  United  States,  is  called  the 
weber,  and  is  equal  to  the  flux  which  is  produced  by  a  M.  M.  F. 
of  one  gilbert  acting  through  a  reluctance  of  one  oersted,  cor- 
responding in  the  above  expression  to  the  ampere,  the  unit  of 
dectric  flux,  which  is  the  electric  flux  or  current  produced  by  an 
E.  M.  F.  of  one  volt  through  a  resistance  of  one  ohm.  For 
example,  if  an  anchor  ring  of  wood,  such  as  is  represented  in 
Fig.  44,  have  a  cross  section  of  10  sq.  cms.  and  be  uniformly 
wrapped  with  insulated  wire,  then  when  the  current  passes 
through  the  winding,  the  magnetic  circuit  will  be  entirely  con- 
fined to  the  interior  of  the  coil  or  solenoid,  and  no  magnetic 
flux  will  be  perceptible  in  the  region  outside  it.  This  is  the 
only  known  form  of  magnetic  circuit  in  which  the  flux-paths 
can  be  confined  to  a  given  channel.  These  flux-paths  are  all 
circular,  and  possess  the  same  intensity  around  each  circle. 
If  the  mean  circumference  of  the  ring  be  60  cms.,  the  reluct- 

ance  of   the    magnetic    circuit   will   be   approximately   -       = 

10 


A 


5° 


ELECT RO-D  YNA MIC  MA  CHINER  Y. 


6  oersteds,  as  in  the  similar  case  of  electric  resistance.  If  the 
number  of  turns  in  the  winding  be  200,  and  the  exciting  current 
steadily  maintained  at  four  amperes,  the  M.  M.  F.  in  the 
magnetic  circuit  will  be  800  ampere-turns,  or  1,005.6  gilberts. 

From  this  the  total  flux  through  the  ring  will  be  —^-'-  =  167.6 
webers. 


FIG.  44. — SECTIONS  OF  WOODEN  RING  UNIFORMLY  WRAPPED  WITH 
INSULATED  WIRE  CARRYING  A  CURRENT. 


50.  Besides  the  case  of  the  anchor  ring,  represented  in  Fig. 
44,  the  magnetic  circuit  of  which,  being  entirely  confined  to 
the  interior  of  the  coil,  permits  its  reluctance  to  be  readily 
calculated,  and  the  flux  to  be  thus  arrived  at,  another  case, 
almost  as  simple,  is  afforded  by  a  long  straight  helix  of  length 
/  cms.,  uniformly  wrapped  with  «,  turns  per  cm.  or  N  =  I  n, 
turns  in  all.  Such  a  helix,  when  excited  by  a  current  of  / 
amperes,  develops  a  M.  M.  F.  of  n  /ampere-turns,  or  1.257  n  I 
gilberts  in  each  centimetre,  or  1.257  N I  gilberts,  for  the  total 
M.  M.  F. 

The  magnetic  circuit  of  such  a  solenoid  is  roughly  repre- 


NON-FERRIC  MAGNETIC  CIRCUITS,  51 

sented  in  Fig.  20  A.  An  inspection  of  this  figure  will  show  that 
flux  passes  through  the  interior  of  the  helix  in  parallel  streams, 
until  it  reaches  a  comparatively  short  distance  from  the  ends, 
when  it  begins  to  sensibly  diverge,  and,  emerging  into  the 
surrounding  space,  is  diffused  through  widely  divergent  paths. 
That  is  to  say,  the  magnetic  circuit  is  characterized  by  two 
distinct  regions;  namely,  that  within  the  coil,  where  the  flux 
is  uniform,  and,  except  near  the  ends,  of  a  maximum  intensity, 
and  that  outside  and  beyond  the  ends  of  the  coil,  where  the 
flux  is  divergent  and  greatly  weakened  in  intensity. 

51.  In  the  case  of  a  long,  straight,  uniformly-wrapped  helix, 
the  reluctance  of  the  circuit  may  be  considered  as  consisting 
of  two  distinct  portions;  namely,  a  straight  portion  occupying 
the  interior  of  the  coil  and  lying  practically  between  the  ends, 
and  a  curved  or  diffused  portion  exterior  to  the  coil.  The 
reluctance  of  the  first,  or  interior  portion,  will  be  practically 

—  oersteds,  where  a,  is  the  cross  sectional  area  of  the  interior 

of  the  coil  in  square  cms.  and  /,  the  length  of  the  coil  in  cms., 
or,  more  nearly,  the  reduced  length  of  the  non-divergent  flux. 
It  will  be  seen,  therefore,  that  the  interior  of  the  coil  behaves 
like  a  straight  wire  carrying  electric  flux,  since  it  practically 
confines  the  flux  to  its  interior,  and,  this  particular  portion  of 
the  magnetic  circuit  is  similar  to  the  case  of  the  anchor  ring 
above  referred  to,  where  the  magnetic  flux  is  confined  to  the 
interior  of  the  ring. 

Since  the  external  circuit  is  diffused,  its  reluctance  cannot  be 
so  simply  expressed.  Its  value,  however,  may  obviously  be 
dealt  with  as  follows  :  although  the  mean  length  of  the  flux- 
paths  outside  the  coil  is  greater  than  in  the  interior  portion, 
yet  the  area  of  cross  section  of  the  circuit  is  enormously 
extended.  It  would  appear,  therefore,  that  in  the  case  of  an 
indefinitely  long  straight  coil,  the  external  reluctance  becomes 
negligibly  small  compared  with  the  internal  reluctance,  and 
may  be  left  out  of  consideration.  In  such  a  case,  therefore, 
the  flux  established  becomes 


1.257  Inl 
l_ 
a 


./r/#  webers  ; 


52  ELECTRO-DYNAMiC  MACHINERY. 

and,  since,  within  the  coil,  this  flux  passes  through  a  cross  sec- 
tional area  of  a  square  centimeters,  the  interior  intensity  will  be 

1.2^7  n  I  a 
(&  =  -  -  =  1.257  n  I  gausses. 


Strictly  speaking,  therefore,  this  is  the  intensity  of  flux  within 
an  indefinitely  long  straight  helix,  and  is  approximately  the 
intensity  within  helices  which  have  lengths  more  than  20  times 
their  diameter. 

52.  We  have  now  discussed  two  cases  of  non-ferric  circuits, 
whose  reluctance  is  readily  calculated;  namely,  a  closed  cir- 
cular coil  and  a  long  straight  helix. 

In  all  other  cases,  the  reluctance  of  a  magnetic  circuit  is 
much  more  difficult  to  compute,  although  the  fundamental 
relations  remain  unchanged. 

When  the  magnetic  circuit  is  non-ferric,  although  the 
reluctivity  of  the  circuit  always  equals  unity,  yet,  owing  to  the 
difficulty  of  determining  the  exact  paths  followed  by  the  diver- 
gent flux,  the  reluctance  is  difficult  to  determine. 

Most  practical  magnetic  circuits,  however,  are  composed 
either  entirely,  or  mainly,  of  iron.  At  first  sight,  the  intro- 
duction of  iron  into  the  circuit  would  appear  to  make  the 
reluctance  more  difficult  to  determine,  because  the  reluctivity 
of  iron  not  only  varies  greatly  with  different  specimens,  but 
also  with  its  hardness,  softness,  annealing,  and  chemical  com- 
position. Moreover,  the  apparent  reluctivity  of  iron  varies 
markedly  with  the  density  of  the  flux  passing  through  it. 
Iron,  when  magnetically  saturated,  possesses  a  reluctivity 
equal  to  that  of  air;  while,  as  we  have  seen,  a*t  low  intensities, 
the  reluctivity  is  much  smaller,  and  may  be  several  thousand 
times  smaller. 

Since,  however,  ferric  circuits,  as  ordinarily  employed, 
practically  confine  their  flux-paths  to  the  substance  of  the 
iron,  and,  since  the  reluctance  of  the  iron  is  so  much  less  than 
the  reluctance  of  the  alternative  air  path  outside,  the  air  flux 
may  usually  be  neglected.  Even  where,  owing  to  the  reluct- 
ance of  the  air  gaps  in  the  circuit,  such  as  in  the  case  of 
dynamos  and  motors,  a  considerable  amount  of  magnetic  leakage 


NON-FERRIC  MAGNETIC  CIRCUITS.  53 

or  diffusion  may  take  place  through  the  surrounding  air,  yet  it 
is  preferable  to  regard  this  leakage  as  a  deviation  from  the 
iron  circuit,  which  may  be  separately  treated  and  taken  into 
account,  and  that  the  flux  passes  principally  through  the 
iron.  For  these  reasons,  ferric  or  aero-ferric  circuits,  at  least 
in  their  practical  treatment,  are  simpler  to  determine  and 
compute  than  non-ferric  circuits,  since,  although  their 
reluctivity  is  variable  at  different  points,  yet  the  geomet- 
rical outlines  of  the  flux-paths  can  be  regarded  as  limited, 
and  the  reluctance  of  these  paths  can  be  readily  determined 
approximately. 

53.  Magnetizing  force  may  be  denned  as  the  space  rate  at 
which  the  magnetic  potential  descends  in  a  magnetic  circuit. 
Since  the  total  fall  of  magnetic  potential  is  equal  to  the  M.  M.  F. 
in  the  circuit,  just  as  the  total  "drop"  in  a  voltaic  circuit  is 
equal  to  its  E.  M.  F.  Consequently,  the  line  integral  or  sum  of 
magnetizing  force  in  a  magnetic  circuit  must  be  equal  to  the 
M.  M.  F.  in  that  circuit.  In  other  words,  if  we  multiply  the 
rate  of  descent  in  potential  by  the  distance  through  which  that 
rate  extends,  and  sum  all  such  stages,  we  arrive  at  the  total 
descent  of  magnetic  potential.  For  instance,  in  Fig.  44  the 
total  difference  of  magnetic  potential  is  1,005.6  gilberts,  which, 
by  symmetry,  is  uniformly  distributed  round  the  entire  circuit. 
Since  the  mean  length  of  this  circuit  is  60  cms.  the  rate  of  fall 

of  potential  is    '  ,         =  16.76  gilberts-per-centimetre  all  round 
oo 

the  ring,  and  this  is,  therefore,  the  magnetizing  force,  or,  as  it 
is  sometimes  called,  the  magnetic  force.  This  magnetizing  force 
is  usually  represented  by  the  symbol  3C,  and,  when  no  iron  or 
magnetic  metal  is  included  in  the  circuit,  is  numerically  iden- 
tical with  the  flux  density  (B,  so  thatOC,  is  expressed  in  gilberts- 
per-centimetre.  The  term  magnetizing  force  was  adopted 
from  the  old  conception  of  magnetic  poles;  for,  if  a  pole  of  unit 
strength  could  be  introduced  into  a  flux  of  intensity  3C  gausses, 
the  mechanical  force  exerted  upon  the  pole  would  be  3C  dynes, 
directed  along  the  flux-paths.  In  any  magnetic  circuit,  if  we 
divide  the  M.  M.  F.  in  gilberts,  by  Jhe  length  of  a  flux-path, 
we  obtain  the  average  value  of  the  magnetizing  force  (or  flux 
density  in  the  absence  of  iron).  Thus,  in  Fig.  21,  if  the  long 


54  ELECTRO-DYNAMIC  MACHINERY. 

helix  there  represented,  has  a  M.M.  F.  of  5,000  gilberts,  and  a 
particular  flux-path  has  a  length  of  500  cms.,  the  mean  magnet- 
izing force,  will  be =  10  gilberts-per-centimetre,  and  the 

500 

mean  flux  density  will  be  10  gausses,  if  there  is  no  iron  in  the 
circuit.  If  there  is  iron,  the  mean  prime  flux  density  or  magnet- 
izing force,  will  still  be  10  gilberts-per-centimetre,  but  the  flux 
density  established  in  the  circuit  will  be  greatly  in  excess  of  10 
gausses. 


CHAPTER  V. 

FERRIC   MAGNETIC    CIRCUITS. 

54.  We  will    now  proceed  to  study   the   phenomena  which 
occur  when  iron  is  introduced  into  a  magnetic  circuit,  as  for 
example,  into  the  circuit  of  the  closed  circular  coil  shown  in 
Fig.  44,  the  mean  interior  circumference  of  which  is  60  cms., 
and  the    mean   cross    sectional   area    10  sq.  cms.      We .  have 
seen  that  if  this  ring  be  excited   with   800   ampere-turns,  or 
1005.6  gilberts,  the  flux  through  the  ring  will  be  167.6  webers; 
or,  since  the  cross  section  of  the  ring  is  ten  square  centimetres, 

the  intensity  will  be  — —   =   16.76  gausses,  and  this  inten- 
10 

sity  would  remain  practically  unchanged  if  the  substance  of 
the  ring  were  copper,  brass,  lead,  zinc,  wood,  glass,  etc. 
When,  however,  the  ring  is  made  of  iron  or  steel,  a  very  marked 
change  takes  place  ;  the  flux  instead  of  being  167.6  webers, 
becomes,  say,  170,000  webers,  with  a  corresponding  increase 
in  intensity.  This  increase  of  flux  in  the  circuit  must  either 
be  due  to  an  increase  in  the  M.  M.  F.,  or  to  a  diminution  in 
the  reluctance.  It  is  usual  to  consider  that  iron  conducts  mag- 
netic flux  better  than  air;  or,  in  other  words,  has  a  greater  mag- 
netic permeability  than  air.  This  idea  corresponds  to  a  reduc- 
tion of  reluctance  similar  to  the  reduction  of  resistance  in  an 
electric  circuit.  Although  generally  accepted,  this  conception 
is  manifestly  incorrect  ;  for  if  the  increased  flux,  due  to  the 
presence  of  iron  in  the  ring,  disappeared  immediately  on  the 
removal  of  the  M.  M.  F.,  there  would  be  no  preponderance  of 
evidence  in  favor  of  either  hypothesis.  But  the  magnetic  flux 
does  not  entirely  disappear  on  the  cessation  of  the  prime 
M.  M.  F.  On  the  contrary,  in  the  case  of  a  closed  iron  ring, 
the  greater  portion  of  the  flux  remains  in  the  condition  called 
residual  magnetism. 

55.  It   is  evident,  therefore,    since    M.   M.   F.  is    necessary 
to  maintain  the  residual  magnetic  flux  in  the  iron,  that  this 


56  ELECTRO-DYNAMIC  MACHINERY. 

M.  M.  F.  is  the  cause  of  the  increase  in  magnetic  flux  when  the 
prime  M.  M.  F.  is   applied,  and  that,  therefore,  the  increased 
flux  cannot  be  due,  except,    perhaps,  in  a  very  small  degree, 
to  any  change  in  the  reluctivity   of  the  medium,  but  to  the 
establishment  of  a  M.   M.  F.  in  the  iron  itself  under  the  influ- 
ence of  the  magnetizing  flux.     It  is  now  almost  certain  that 
the  ultimate  particles  of  the  iron,  the  molecules,  or  the  atoms, 
are  all  initially  magnets  ;  /.  e.,  inherently  possess  M.  M.  Fs. 
and  magnetic  circuits.     The  origin  of  this  molecular  magnetism 
in  iron  is,  however,  not  yet  known.     In  the  natural  condition, 
all  the  separate  magnets  of  which  iron  is  composed,  are  dis- 
tributed  indifferently  in  all    directions,  so  that  their  circuits- 
neutralize    one   another  and  produce  no  appreciable  external 
effects.     Under  the  influence  of  a  magnetizing  flux,  these  mole- 
cular magnets  tend  to  become  aligned,  and  to  break  up  their 
original  groupings.     As  they  become  aligned,  and  their  M.  M. 
Fs.   become  similarly  directed,  they  are  placed  in  series,  and 
their  effects  are  rendered  cumulative,  so  that  they  exercise  an 
increasing  external  influence,  and  an  extending  external  flux. 
Or,    taking'  the  hydraulic  analogue  already  referred  to,    and 
regarding  each   separate  molecular  magnet  as  a  minute  ether 
pump,  as  all  the  ether  pumps  are  brought  into  line,  the  streams 
they  are  able  to  direct  are  increased  in  velocity,  and  are,  there- 
fore,   carried    further   into    the    surrounding    space.      Conse- 
quently, the  flux  produced  in  the  magnetic  ring  shown  in  Fig. 
44,  when  furnished  with  an  iron  core,  may  be  regarded  as  aris- 
ing from  two  distinct  sources  of  M.  M.  F. ;  namely, 

(i.)  The  prime  M.  M.  F.y  or  that  due  to  the  magnetizing 
current  which  produces  the  flux  through  the  circuit  and  sub- 
stance of  the  iron,  the  value  of  which  is  practically  the  same 
as  though  the  core  were  of  wood  or  Other  non-magnetic 
material.  This  flux  may  oe  called  the  prime  flux  and  possesses 
a  corresponding  prime  intensity.  In  the  case  considered,  the 
prime  intensity  or  magnetizing  flux  density  is  16.76  gausses. 
This  magnetic  intensity,  acting  upon  the  molecules  of  the  iron, 
produces: 

(2.)  The  induced  M.  M.  P.,  which  may  be  called  the  aligned 
or  structural  M.  M.  F.,  and  depends  for  its  magnitude  not  only 
upon  the  quality  of  the  iron,  but  also  upon  the  intensity  of  the 
prime  flux.  The  harder  the  iron,  and  the  greater  its  mecham- 


FERRIC  MAGNETIC  CIRCUITS. 


57 


cal  tendency  to  resist  molecular  distortion,  the  greater  must  be 
the  prime  intensity  or  the  magnetic  distorting  power,  in  order 
to  bring  about  the  full  structural  M.  M.  F.  When  the  prime 
intensity  has  reached  such  a  magnitude  that  all  the  separ- 
ate molecular  magnets  in  the  iron  are  similarly  aligned,  the 
iron  is  said  to  be  saturated,  and  the  M.  M.  F.  it  produces  is  a 
maximum,  and,  on  the  removal  of  the  prime  M.  M.  F.  the 
structural  M.  M.  F.  will,  in  the  case  of  a  closed  ring,  largely 
remain,  especially  if  the  ring  be  of  hard  iron  or  steel.  If,  on 


FIG.  45. — IRON   RING   PROVIDED   WITH    AIR-GAP,  AND   WOUND    WITH    WIRE. 

the  contrary,  the  ring  be  of  soft  iron,  and  have  an  air-gap  cut 
in  it,  the  structural  M.  M.  F.  may  largely  disappear.  The 
relation  between  the  structural  M.  M.  F.  and  its  flux,  and  the 
prime  M.  M.  F.  and  the  intensity  which  produces  it,  is  complex, 
and  can  only  be  ascertained  by  experimental  observation. 

56.  Fig.  45  represents  the  same  iron  ring  with  a  saw-cut  or 
air-gap  at  A,  having  a  width  of  0.5  cm.  The  reluctance  of 
this  air-gap,  which,  neglecting  diffusion,  has  a  length  of  0.5 

cms.  and  a  cross-section  of  10  sq.  cms.  is  — —  =  o.oq  oersted.     If 

10 

the  total  structural  M.  M.  F.,  established  in  the  ring  under 
excitation,  be  180,000  gilberts,  then,  immediately  on  the  with- 


58  ELECTRO-DYNAMIC  MACHINERY. 

drawal  of  the  prime  M.  M.  F.,  the  residual  flux   through  the 

circuit   will    be       0'000  =  30,000   webers.     Where   this   flux 
o 

passes  through  the  reluctance  of  the  air-gap  there  will  be 
established  a  C.  M.  M.  F.,  just  as  in  the  electric  circuit  where 
a  current  of  /  amperes  passes  through  a  resistance  of  R,  ohms, 
there  is  established  a  C.  E.  M.  F.  of  I  R  volts.  So  that 
the  C.  M.  M.  F.  has  in  this  case  the  value,  F  =  $  R  = 
30,000  x  0.05  =  1,500  gilberts.  This  C.  M.  M.  F.  represents 

a    mean    demagnetizing  force    of    ~-~ —   =   25    gilberts-per- 

centimetre,  through  the  iron  circuit.  If  this  intensity  of  de- 
magnetizing force  is  sufficient  to  disrupt  the  structural  align- 
ment of  the  molecular  magnets,  the  residual  magnetism  will 
disappear.  If,  however,  the  intensity  be  less  than  that  which 
the  hardness  of  the  iron  requires  to  break  up  its  structure,  the 
residual  magnetism  will  be  semi-permanent. 

Even  though  it  be  admitted  that  the  preceding  represents 
the  true  condition  of  affairs,  and  though  it  is  the  only  existing 
hypothesis  by  which  the  phenomena  of  residual  magnetism  can 
be  accounted  for,  nevertheless,  for  practical  computations 
connected  with  dynamo  machinery,  it  is  more  convenient  to 
assume  that  there  is  no  structural  M.  M.  F.  in  iron,  and  that 
the  difference  in  the  amount  of  flux  produced  in  ferric  circuits 
is  a  consequence  of  decreased  reluctance  in  the  iron;  or,  in 
other  words,  that  iron  is  a  better  conductor  of  magnetism. 
We  will,  therefore,  in  future,  adopt  the  untrue  but  more  con- 
venient hypothesis. 

57.  The  reluctivity  of  iron  may  be  as  low  as  0.0005,  but 
varies  with  the  flux  density  ;  that  is  to  say,  the  reluctance  of  a 
cubic  centimetre  of  iron,  measured  between  parallel  faces,  may 
be  as  low  as  0.0005  oersted. 

58.  The  fact  has  been  established  by  observation,  that  in  the 
magnetic  metals,  within  the  limits  of  observational   error,  a 
linear  relation  exists  between  reluctivity  and  magnetizing  force. 
That  is  to  say,  within  certain  limits,  as  the  magnetizing  force 
brought  to  bear  upon  a  magnetic  metal  increases,  the  apparent 
reluctivity  of  the  metal  increases  in  direct  proportion.     Thus, 
taking  the  case  of  soft  Norway  iron,  its  reluctivity,  at  a  mag- 


FERRIC  MAGNETIC  CIRCUITS. 


59 


ic 


netizing  force  of  4  gilberts-per-centimetre,  or  prime  magnet^ 
intensity  of  4  gausses,  may  be  stated  as  0.0005.  Increasing 
the  mao-netizinp-  force,  the  reluctivitv  increases  bv  0.000.0^7 


lIllcllMLy     ui    4    gausses,    may     uc    »LaLc\a    as    w.^ww^j.        j.in_-ica: 

the  magnetizing  force,  the  reluctivity  increases  by  o.ooo. 


057 


I.  Ordinary  Sample  of  Dynamo  Cast  I ron(Kennelly)?'=0.0026+ 0.000093  3v 
II.  Sample  of  Dynamo  Wrought  Iron  "         Y=Q. 0004+  0.000057 3C 

III.  Sample  of  Annealed  Norway  Iron  «         f=0.0003+  0.000057  JC 

|IV.        ..  Soft  Iron  (  Stoletow)K=0. 0002+ 0.000056  3C 

-V.        »  Norway  Iron  (RowlandJ^O.OOOl  +  0.000059  JC 


X 


10  20  30  40  50  60  70  80 

MAGNETISING  FORCEjC(PRrME  FLUX  DENSITY)  GAUSSES 

FIG.  46.  —  CURVES   OF   RELUCTIVITY    IN   RELATION   TO    MAGNETIZING    FORCE. 

per  gauss,   and  this  increase,   plotted  graphically,    would   be 
represented  by  a  straight  line. 


59.  The  accompanying  curve  sheet   represents   the   results 
of  actual   observations  by  different  observers   upon  different 


60  ELECTRO-DYNAMIC  MACHINERY. 

samples  of  soft  wrought  iron  and  cast  iron.  It  will  be  seen  that 
in  the  early  stages  of  magnetization,  below  a  critical  magnetiz- 
ing force,  which  varies  with  different  samples  from  i  to,  perhaps, 
15  gilberts-per-centimetre,  corresponding  to  a  prime  magnetic 
intensity  of  i  to  15  gausses  (the  latter  in  the  case  of  cast  iron), 
the  reluctivity  decreases  with  an  increase  in  magnetizing  force; 
but,  when  the  critical  magnetizing  force  is  reached,  the  direction 
of  the  curve  changes  and  the  value  becomes  linear.  Strictly 
speaking,  the  linear  relation  of  reluctivity  and  magnetizing  force, 
represented  in  the  figure,  is  true  only  for  the  apparent  reluc- 
tivity of  the  metal  itself,  and  is  irrespective  of  the  ether  which 
pervades  the  metal;  for,  were  this  relation  strictly  linear  for  all 
values  of  the  magnetizing  force  beyond  the  critical  value,  the 
reluctivity  would  become  infinite  with  an  infinite  magnetizing 
force  ;  whereas,  by  observation,  the  reluctivity  of  the  most 
highly  saturated  iron  never  exceeds  unity,  that  of  the  air  pump 
vacuum,  or  practically  that  of  air.  In  point  of  fact  we  may 
consider  the  magnetism  as  being  conducted  through  two  paths 
in  multiple  ;  namely,  that  of  the  magnetic  metal  proper,  and 
that  of  the  ether  permeating  the  metal.  The  first  path  may 
be  called  the  ferric  path  of  metallic  reluctivity,  and  has  a  reluc- 
tance varying  from  a  minimum  at  the  critical  magnetizing  force, 
up  to  infinity,  by  the  linear  relation.  The  second  is  the  ether 
path  of  reluctivity,  and  may  be  assumed  to  have  a  constant 
reluctivity  of  unity.  The  joint  reluctivity  of  the  two  paths  will 

j     \/     -y  i? 

be  -     —  =  — - —  where  v.  is  the  reluctivity  of  the  ferric  path, 
i  -j-  v       i  -\-v 

Since  in  actual  dynamo  machinery  the  value  of  the  magnetiz- 
ing force  is  never  much  more  than  80  gilberts-per-centimetre, 
the  above  consideration  is  of  small  practical  importance,  since 
v  is,  always  much  less  than  unity,  say  o.oi,  and  the  discrepancy 
introduced  by  taking  account  of  the  multiple-connected  ether 

path,  is  only  the  difference  between  o.oi  and    — '- =  - — 

i  -{-  o.oi        i.oi 

or  about  i  per  cent,  so  that,  for  all  practical  purposes,  we  may 
assume  that  the  metallic  reluctivity  is  the  actual  reluctivity  of 
the  iron. 

Beyond  the  critical  magnetizing  force,  therefore,  the  value 
of  the  metallic  reluctivity  may  be  readily  obtained  by  the  equa- 
tion v  —  a  -j-  ^3C,  where  a,  is  the  reluctivity  which  would  exist 


FERRIC  MAGNETIC  CIRCUITS.  6 1 

at  zero  magnetizing  force,  if  the  linear  relation  held  true  below 
the  critical  value,  and  £,  is  the  increase  in  reluctivity  per  gauss 
of  prime  magnetizing  intensity  expressed  by  3C.  According  to 
the  present  accepted  values  of  the  C.  G.  S.  system,  reluctivity 
is  a  numeric,  and  its  value  never  exceeds  unity  ;  thus  for 
wrought  iron  a  —  0.0004,  and  b  =  0.000,057. 

60.  If  the  ring- shown  in  Fig.  44  be  composed  of  wood,  and 
be  excited  by  1,000  ampere-turns  =  1,257  gilberts,  then,  since 
its  mean  length  of  circuit  (circumference)  is  60  cms.,  and  cross 
sectional  area  10  sq.  cms.,  its  reluctance  will  be  6  oersteds,  the 

flux    *         =  209.5  webers,    and   the   intensity  — ^-  =  20.95 
6  10 

gausses,  so  that  the  magnetic  force  has  a  rate  of  descent  of  mag- 

'netic  potential,  the  uniform  distribution  of  which  is    *         = 

oo 

20.95  gilberts-per-centimetre.  Strictly  speaking,  the  intensity 
of  the  magnetic  flux  is  not  uniform  over  all  portions  of  the  area 
of  cross  section  of  the  core,  being  denser  at  the  inner  circum- 
ference and  weaker  at  the  outer  circumference.  For  example, 
if  the  inner  circumference,  instead  of  being  60  cms.,  which  is  the 
mean  value,  be  58  cms.,  the  gradient  of  magnetic  potential  will 

be  uniformly     '         =  21.67   gilberts-per-centimetre,   and   the 

5° 
intensity,  21.67  gausses;  while,  if  the  outer  circumference  be 

62  cms., -the  intensity  at  that  circumference  will  be     *         — 

02 

20.27  gausses.  Since,  however,  all  such  existing  differences  of 
intensity  can  be  made  negligibly  small,  by  sufficiently  increas- 
ing the  ratio  of  the  size  of  the  ring  to  its  cross  section,  we 
may,  for  practical  purposes,  omit  them  from  consideration. 

61.  Suppose   now   the    core   of  the  ring   be    composed   of 
.soft  Norway  iron  instead  of  wood;  then  from  the  preceding 
curves,  or  the  equation, 

v  =  0.0004  -f-  0.000,057  3C, 
we  find  that  at  this  mean  intensity  of  3C  =  20.95 
v  =  0.0004  +  0.001194  =  0.001594, 

or  about  ; — th  of  that  of  air.     The  mean  length  of   the   cir- 
600 


62  ELECTRO-DYNAMIC  MACHINERY. 

cuit  being  60  cms.,  and  its  area,  as  before  mentioned,  10  sq. 
cms.,  its  reluctance,  under  these  circumstances,  will  be  —  x 
0.001594  =  0.009564  oersted,  and  the  flux  in  the  circuit 

— *'2"     =    131,430   webers,    with  an  intensity  of — 

0.009564  10 

13,143  gausses. 

62.  If  the  core  of  the  ring  instead  of  being  of  soft  Norway  iron 
be  made  of  cast  iron,  the  reluctivity,  at  JC  =  20.95,  would  be 
approximately,  0.0046,  and  the  reluctance  of  the  circuit  0.0276 
oersted,  making  the  total  flux  45,540  webers,  with  an  intensity 
of  4,554  gausses,  or  about  three  times  less  than  with  soft  Nor- 
way iron.     The  practical  advantages,  therefore,  of  construct- 
ing cores  of  soft  Norway  iron,  rather  than  of  cast  iron,  is  man- 
ifest, when  a  high  intensity  is  required. 

63.  It  is  important  to  remember  that  the  entire  conception 
of  metallic  reluctivity  is  artificial,  and  that  although  very  con- 
venient for  purposes  of  computation,  yet  as  already  pointed  out, 
it  is  incompetent  to  deal  with  the  case  of  residual  magnetism. 
Thus,  if  the  prime  M.  M.  F.  from  an  iron  ring  be  withdrawn,  we 
should  expect  the  flux  to  entirely  disappear,  whereas  we  know 
that  a  large  proportion  will  generally  remain.     Since,  however, 
electro-dynamic  machinery  rarely  calls  residual  magnetism  into- 
account,  the  reluctivity  theory  is  adequate  for  practical  pur- 
poses beyond  critical  magnetizing  forces. 

64.  As  another  illustration,  let  us  consider  a  very  long  rod 
of  iron,  wound  with  a  uniform  helix.     Here,  as  we  have  already 
seen,   disregarding  small  portions   near  the  extremities,    the 
intensity   may   be     regarded    as    uniform    within    the    helix. 
Since  the  reluctance  of  the  external  circuit  may  be  neglected, 
this  flux  density  is  1.257  n  i,  gausses,  where  n,  is  the  number 
of  loops   in  the   helix  per  centimetre  of  length,  and  /',  is  the 
exciting   current   strength    in   amperes.       Or,    regarding   the 
intensity  as  being  numerically  equal  to  the  gradient  of  mag- 
netic potential,  which  changes  steadily  by  1.257  n  /,  per  centi- 
metre (this  being  the  number  of  gilberts  added  in  the  circuit 
per  centimetre  of  length,  the  fall  of  potential  or  drop  in  the 


FERRIC  MAGNETIC    CIRCUITS.  63 

external  circuit  being  negligible),  the  gradient,  within  the  helix, 
is  1.257  n  i  gausses  as  before.  A  rod  of  Norway  iron  i 
metre  long  and  2  cms.  in  diameter,  wound  with  twenty  turns 
of  wire  to  the  centimetre,  carrying  a  current  of  i  ampere, 
would,  at  this  magnetizing  force,  have  an  intensity  in  it  of 
approximately  1.257  x  20  x  i  =  25.14  gausses.  The  reluc- 
tivity of  Norway  iron  would  be  by  the  preceding  formula 

v  =  0.0004  -}-  0.000,057    X   25.14  =  0.001833  or  about  —  th 

of  air.  The  length  of  rod  being  100  cms.,  and  its  cross  section 
3.1416  square  cms.,  the  reluctance  would  be  approximately 

-  -  -  x  0.001833  —  0.05836  oersted.  The  total  M.  M.  F. 
3.1416 

being  100  X  20  X  i  =  2,000  ampere-turns  =  2,514  gilberts. 
The  flux  in  the  circuit,  assuming  that  the  reluctance  of  the  air 
path  outside  the  bar  may  be  neglected,  is,  approximately, 

2>  =  43,070  webers,  with  an  intensity  of  43      °  =  13,710 


gausses. 

65.  In  cases  where  the  flux  is  confined  to  definite  paths,  as 
in  a  closed  circular  coil,  or  in  a  very  long,  straight,  and  uni- 
formly wrapped  bar,  the   preceding  calculations  are  strictly 
applicable*.     When,  however,  an  air-gap  is  introduced  into  the 
closed  ring,  that  is,  when  its  circuit  becomes  aero-ferric,  the 
results   begin   to   be   vitiated,    partly   owing  to  the  influence 
of  diffusion,    and   partly   to  the  results   of  the  C.   M.  M.  F. 
which  is  established  at  the  air-gap.     As  the  length  of  the  air- 
gap  increases,  the  degree  of  accuracy  which  can  be  attained 
by  the  application  of  the  formula  diminishes,  but  in  dynamos, 
the  aero-ferric  circuits  are  in  almost  all  cases  of  such  a  char- 
acter, that  the  degree  of  approximation,  which  can  be  reached 
by  these  computations,  is  sufficient  for  all  practical  purposes; 
for,   while  it  is  impossible  strictly  to  compute  the  magnetic 
circuit  of  a  dynamo  by  any  means  at  present  within  our  reach, 
yet  the  E.  M.  F.  of  dynamos,  and  the  speed  of  motors,  can  be 
predicted   by   computation   within   the    limits  of   commercial 
requirements. 

66.  If  the  ring  of  Fig.  45  be  provided  with  a  small  air-gap  of 
0.5  cm.  in  width,  the  intensity  in  the  circuit,  before  the  intro- 


64  ELECTRO-DYNAMIC  MACHINERY. 

duction  of  the  iron  core,  will  be  practically  unchanged  by  the 
existence  of  the  gap,  that  is  to  say,  with  the  same  1,000  ampere- 
turns,  or  1,257  gilberts  of  M.  M.  F.,  the  prime  intensity  exist- 
ing in  the  ring  will  be  practically  20.95  gausses.  In  Ihe  air- 
gap  itself,  the  intensity  will  be  less  than  this,  owing  to  lateral 
diffusion  of  the  flux;  but,  neglecting  these  influences,  we  may 
consider  the  intensity  to  be  uniform.  Now,  introducing  a  soft, 
Norway  iron  core  into  the  ring,  the  iron  is  subjected  to  an 
intensity  of  approximately,  20.95  gausses  throughout  the  cir- 
cuit. The  reluctivity  of  the  iron  at  this  intensity,  is,  as  we 
have  seen,  0.001596.  The  length  of  the  circuit  in  the  iron 
will  be  59.5  cms.,  and  its  cross  section  10  sq.  cms.,  making  the 

ferric  reluctance  A?l£_  x  0.001594  =  0.009484  oersted.       The 
10 

reluctance  of  the  air-gap,  neglecting  the  influence  of  lateral 
diffusion,  will  be  —  X  i  =0.05  oersted,  and  the  total  reluct- 
ance of  the  circuit  therefore,  will  be  0.009484  +  0.05  = 

0.059484  oersted.     The  flux  in  the  circuit  will  be  — '      0     = 

0.059484 

21,130  webers,  and  the  intensity  in  the  iron,  2,113  gausses. 
The  existence  of  the  air-gap  has,  therefore,  reduced  the  flux 
from  131  kilowebers  to  21  kilowebers. 

67.  In  practical  cases,  however,  the  problem  which  presents 
itself  is  not  to  determine  the  amount  of  flux  produced  in  a 
magnetic  circuit  under  a  given  magnetizing  force,  but  rather 
to  ascertain  the  M.  M.  F.,  which  must  be  impressed  on  a  cir- 
cuit in  order  to  obtain  a  given  magnetic  flux.  When  the  total 
required  flux  in  a  circuit  is  assigned,  the  mean  intensity  of  flux 
in  all  portions  of  the  circuit  is  approximately  determinable, 
being  simply  the  flux  divided  by  the  cross  section  of  the  circuit 
from  point  to  point.  What  is  required,  is  the  reluctivity  of  iron 
at  an  assigned  flux  density  and  this  we  now  proceed  to  determine. 

ftr> 

From  the  equations,  v  =  a  -\-  b  3C,  and  (B  = —  ,  correspond- 
ing in  a  magnetic  circuit,  to  /  = in  the  electric  circuit,  /, 

being  the  electric  flux  density  or  amperes-per-sq.-cm.  and  pf 
the  resistivity,  we  obtain,  v  = — 


FERRIC  MAGNETIC  CIRCUITS.  65 

This  equation  gives  the  reluctivity  of  any  magnetic  metal 
for  any  value  of  the  flux  density  &  passing  through  it,  when 
the  value  of  the  constants  a  and  £,  have  been  experimentally 
determined.  The  values  of  v,  so  obtained  are  only  true  for 
reluctivities  beyond  the  critical  value,  where  the  linear  relation 
expressed  in  the  equation  v  =  a  -f-  b  5C  commences. 

68.  The  following  table  gives  the  values  of  the  reluctivity 
constants  a  and  <£,  for  various  samples  of  iron  : 


Sample. 

a 

b 

Observer. 

Soft  Iron,     .         .         .. 

.,     •   .      0.000,2 

0.000,056 

Stoletow. 

.      O.OOO,! 

0.000,059 

Rowland. 

O  OOO  O^Q^ 

Fessenden. 

<  <       (i 

.      O.OOO,2275 

^  •  *-**-«-*  ,  \j  3  \j  j 
0.000,0654 

« 

"       " 

.      0.000,3325 

O.OOO,O64 

11 

«       « 

.      O.OOO,2I3 

0.000,05605 

" 

Cast  Steel,    . 

.     0.000,45 

0.000,05125 

" 

«       <« 

.     0.000,314 

0.000,0563 

" 

Mitis  Iron,  . 

.     0.000,25 

0.000,0575 

it 

Cast  Iron,     .      .    . 

.     0.001,031 

0.000,129 

" 

Improved  Cast  Iron,     . 

.     0.000,9025 

O.OOO,IO6 

it 

Wrought  Iron, 

.     0.000,22 

O.OOO,O58 

Hopkinson. 

Dynamo  Wrought  Iron, 

.     0.000,4 

0.000,057 

Kennelly. 

"        Cast  Iron, 

.       0.002,6 

O.OOO,O93 

M 

Annealed  Norway  Iron, 

.     0.000,3 

O.OOO,O57 

U 

69.  Fig.  47  shows  curves  of  reluctivity  of  various  samples 
of  iron  and  steel  at  different  flux  densities.     The  descending 
branches  are  of  practically  little  importance  in  connection  with 
dynamo-electric  machinery.     They  are  included  in  the  curves, 
however,  in  order  to  bring  these  into  coincidence  with   actual 
observations.      It  will  be  seen,  that  while  the   reluctivity  of 
Norway  iron  is  only  0.000,5  at  8  kilogausses,  that  of  cast  iron 
is  commonly  about  o.oio,  or  twenty  times  as  great. 

70.  In  order  to  show  the  application  of  the  above  curves  of 
reluctivity,  we  will  take  the  simplest  case  of  the  ferric  circuit; 
namely,    that  of  a  soft  Norway  iron  anchor  ring,    shaped  as 
shown  in  Fig.  44,  of   10  square  centimetres   cross   section  and 
60  cms.  mean  circumference,  uniformly  wrapped  with  insulated 
wire.     If  it  be  required  to  produce  a  total  flux  of  80  kilowebers 
in  this  circuit,  the  intensity  in  the  iron  will  be  8  kilogausses, 


66 


ELECTRO-DYNAMIC  MACHINERY. 


0.012 


7          8 
Kilogausses  Flux  Density  in  Iron 

URVES   OF   RELUCTIVITY    IN    RELATION   TO    FLUX    DENSITY. 


17     J18 


and,  by  following  the  curve  for  Norway  iron,  in  Fig  47,  it  will 
be  seen  that  its  reluctivity  at  this  density  is  0.000,5.  The  re- 
luctance of  the  circuit,  therefore,  will  be  —  X  0.000,5  —  °-°°3 


FERRIC  MAGNETIC  CIRCUITS.  67 

oersted,  and  the  M.  M.  F.  necessary  to  produce  the  requisite 
magnetic  flux  will  be  £F  =  $  (R  =  80,000  x  0.003  =  24°  &l~ 
berts,  or  240  x  0.7958  =  191  ampere-turns. 

71.  If,  however,  the  ring  be  of  cast  iron,  instead  of  soft  Nor- 
way iron,  its  reluctivity  at  this  density  would  be  say  o.oio, 

and  its  reluctance  - —  x  o.oio  =  0.06  oersted,  from  which  the 
10 

required  M.  M.  F.  will  be  80,000  X  0.06  =  4,800  gilberts  = 
3,820  ampere-turns.  The  importance  of  employing  soft  iron 
for  ferric  magnetic  circuits,  in  which  a  large  total  flux  is  re- 
quired, will,  therefore,  be  evident. 


OF  THE 
TJNIVERSITT 


CHAPTER  VI. 

AERO-FERRIC    MAGNETIC    CIRCUITS. 

72.  We  will  now  consider  the  case  of  the  aero-ferric  magnetic 
circuit.     Fig.  48  is  a  representation  of  a  simple  ferric  circuit 
consisting  of  two  closely  fitting  iron  cores,  the  upper  of  which 
is  wrapped  with  a  magnetizing  coil  M.     The  polar  surfaces 
are  made  to  correspond  so  closely,  that  when  the  coil  M,  has 
a  magnetizing  current  sent  through  it,  the  magnetic  attraction 
between  the  two  cores  will  cause  them  to  exclude  all  sensible 
air-gaps.     The  general  direction  of  the  flux-paths  is  shown  by 
the  dotted  arrows,  and   a  mechanical  stress  is  exerted  within 
the  iron  along  the  flux-paths. 

These  stresses  cannot  be  rendered  manifest,  so  long  as  the 
iron  is  continuous.  In  other  words,  the  continuous  anchor  ring, 
as  shown  in  Fig.  44,  would  give  no  evidence  of  the  existence  of 
stress  along  its  flux-paths.  In  the  case  shown  in  Fig.  48,  the 
stress  is  rendered  evident  by  the  force  which  must  be  applied  to 
the  two  magnetized  cores  in  order  to  separate  them.  The  amount 
of  this  force  depends  upon  the  magnetic  intensity  in  the  iron 
at  the  polar  surfaces,  and,  if  (B,  represents  this  intensity  in 
gausses,  the  attractive  force  exerted  along  the  flux-paths  at  the 

/T>2 

polar  surfaces;  /.   e.,   perpendicularly  across  them,  will  be  =r— ^ 

dynes-per-square-centimetre  of  polar  surface.  The  dyne  is  the 
fundamental  unit  of  force  employed  in  the  system  of  C.  G.  S. 
units  universally  employed  in  the  scientific  world,  and  is  equal 
to  the  weight  of  1.0203  milligrammes  at  Washington;  that  is 
to  say,  the  attractive  force  which  the  earth  exerts  upon  one 
milligramme  of  matter,  is  approximately,  equal  to  one  dyne. 

73.  If  the  magnetic  circuit  shown  in  Fig.  48  has  a  uniform 
area  of  cross  section   of  12  square  centimetres,  and  the  mag- 
netic intensity  in  the  circuit  be  everywhere   17   kilogausses, 

68 


AERO-FERRIC  MAGNETIC  CIRCUITS. 


69 


then  the  attractive  force  exerted  across  each   square   centi- 
metre of  the  polar  surfaces  at  Rlt  and  R^  will  be 

17,000  X  17,000 


8  x  3-J416 


=  11,500,000  dynes, 


or    11,500,000  X  1.0203  =  11,730,000  milligrammes  weight  = 
11,730  grammes  weight  =  25.86  Ibs.  weight. 
As  there  are  twelve  square  centimetres  in  each  polar  surface,, 


6,324  VOLTS 
7-0.081  OHM 

0.00029  OHM  O.C0023  OHM 


1  =  204,000  AMPERES 

FIGS.    48   AND  49. — DIAGRAMS   REPRESENTING  A   SIMPLE   FERRIC,  AND   AN 
AERO-FERRIC,  CIRCUIT,    AND   THEIR   ELECTRIC   ANALOGUES. 

the  total  pull  across  each  gap  will  be  12  x  25.86  =  310.32  Ibs. 
weight;  and  since  there  are  two  gaps,  the  total  pull  between 
the  iron  cores  will  be  620.64  Ibs.  weight,  so  that,  if  the  whole 
magnet  were  suspended  in  the  position  shown  in  Fig.  48,  this 
weight  should  be  required  to  be  suspended  from  the  lower  core 
(less,  of  course,  the  weight  of  the  lower  core)  in  order  to  effect 
a  separation;  or,  in  other  words,  this  should  be  the  maximum 
weight  which  the  magnet  could  support. 

74.  In  order  to  ascertain  the  M.  M.  F.   needed  to  produce 

the  required  intensity  of  17  kilogausses  through  the  circuit  in 

order  to  cause  this  attraction,  we  find,  by  reference  to  Fig.  47, 

that  the  reluctivity  of  Norway  iron  at  this  intensity  is  0.0073; 

73 


10,000 


that  of  air.     The  reluctance  of  the  magnetic  cir- 


70  ELECTRO-DYNAMIC  MACHINERY. 

CQ 

cuit  will,  therefore,  be  --  X  0.0073  =  0.03042   oersted.     The 

total  flux  through  the  circuit  will  be  17,000  x  12  =  204,000 
webers,  and  the  M.  M.  F.  required  to  produce  the  flux,  there- 
fore, will  be  204,000  x  0.03042  =  6,206  gilberts,  or  6,206  x 
0.7958  =  4,937  ampere-turns.  If,  then,  the  coil  J/,  has  2,000 
turns,  it  will  be  necessary  to  send  through  it  a  current  of 
2.469  amperes,  in  order  to  produce  the  flux  required. 

The  electric  circuit  analogue  of  this  case  is  represented  in 
the  same  figure,  where  E,  represents  the  E.  M.  F.  in  the  electric 
circuit  as  a  voltaic  battery,  and  the  amount  of  this  E.  M.  F. 
necessary  to  produce  a  current  of  strength  /,  amperes,  when  the 
total  resistance  of  the  circuit  is  r,  ohms,  will  be  E  =  i  r  volts. 

75.  So  far  we  have  considered  that  no  sensible  reluctance 
existed  at  the  polar  surfaces  Rl9  and  R^.  Practically,  how- 
ever, it  is  found,  that,  no  matter  how  smooth  the  surfaces  may 
be,  and,  therefore,  how  closely  they  may  be  brought  into  con- 
tact, a  small  reluctance  does  exist,  owing,  apparently,  to  the 
absence  of  molecular  continuity. 

This  reluctance  has  been  found  experimentally,  in  case  of 
very  smooth  joints,  to  be  equivalent  to  the  reluctance  of  an 
air-gap,  from  0.003  to  0.004  cm.  wide  (0.0012"  to  0.0016"). 
Taking  this  reluctance  into  account  we  have  at  R^  and  at  R^ 
an  equivalent  reluctance  of  air  path,  say  0.0035  cm-  l°ng  and 
12  cms.  in  cross-sectional  area.  Since  the  reluctivity  of  air 

is  unity,  the  reluctance  at  each    gap   becomes 


0.000,29  oersted,  and  the  reluctance  of  the  circuit  has,  there- 
fore, to  be  increased  by  0.000,58  oersted,  making  a  total  of 
0.03042  -f-  0.000,58  =  0.031  oersted,  and  requiring  the  M.  M. 
F.  of  204,000  x  0.031  or  6,324  gilberts  =  5,032  ampere-turns, 
or  an  increase  of  current  strength  to  2.516  amperes. 

,76.  It  is  evident,  since  the  attractive  force  exerted  across  a 

/02 

square  centimetre  of  polar  ^surface  is  equal  to  —   dynes,    that 

STT 

doubling  the  intensity  at  the  polar  surface  will  quadruple  the 
attraction  per  square  centimetre.  Therefore,  all  electro- 
magnets, which  are  intended  to  attract  or  support  heavy 
weights,  are  designed  to  have  as  great  a  cross-sectional  area 


AERO-FERRIC  MAGNETIC  CIRCUITS.  71 

of  polar  surface  as  possible,  combined  with  a  high  magnetic  in- 
tensity across  these  surfaces.  If,  however, *the  increase  of  the 
area  of  polar  surface  is  attended  by  a  corresponding  diminu- 
tion of  flux  density,  the  total  attractive  force  across  the  surface 
will  be  diminished,  because  the  intensity,  per-unit-area,  will  be 
reduced  in  the  ratio  of  the  square  of  the  intensity,  while  the 
pull  will  only  increase  directly  with  the  surface.  It  is  evident, 
therefore,  that  soft  iron  of  low  reluctivity  is  especially  desira- 
ble in  powerful  electro-magnets. 

If,  for  example,  cast  iron  was  employed  in  the  construction 
of  the  magnet  of  Fig.  48,  instead  of  soft  Norway  iron,  and  the 
same  M.  M.  F.,  namely,  6,324  gilberts  were  applied,  the  mean 
magnetizing  force  would  be  this  M.  M.  F. ,  divided  by  the  mean 

length  of  the  circuit  in  cms.,  or  X  —      >3      =  126.48  gilberts- 

per-centimetre. 

At  this  magnetizing  force,  a  sample  of  cast  iron  would  have  a 
reluctivity  represented  by  the  formula  v  =  (a  -j-  ^5C), where  a, 
may  be  0.0027,  and  £,  0.000,09,  so  tnat  its  reluctivity  at  133.92 
gilberts  per  centimetre  of  magnetizing  force  would  be  (0.0027  -f- 
0.000,09  X  126.48)  =  0.01407.  The  reluctance  of  the  cast  iron 
circuit,  including  the  small  reluctance  in  the  air-gaps,  would  be 

5° 

-—  X  0.01407  =0.05863  oersted,  and  the  flux  in  the  circuit  would 

be  '  -=  108,700  webers,  or  an  intensity  of  9,058  gausses. 
The  magnetic  attraction  between  the  surfaces  per-square- 
centimetre,  would,  therefore,  be  — ^— ^  =  3,264,000 

dynes,  or  3, 331  grammes  weight,  or  7.342  Ibs.  weight;  and,  since 
the  total  polar  surface  amounts  to  24  square  centimetres,  the 
total  attractive  force  exerted  between  and  across  them  is 
176.2  Ibs.  weight.  The  effect  of  introducing  cast  iron  instead 
of  wrought  iron  into  the  magnetic  circuit,  keeping  the  dimen- 
sions and  M.  M.  F.  the  same,  has,  then,  been  to  reduce  the 
total  pull  from  620.64  Ibs.  to  176.2  Ibs.,  or  71.6  per  cent. 

77.  If  now  an  air-gap  be  placed  in  the  circuit  at  JRl9  and  JR^ 
of  half  an  inch  (1.27  cm.)  in  width,  as  in  Fig  49,  two  results  will 
follow;  viz., 


72  ELECTRO-DYNAMIC  MACHINERY. 

(i.)  A  greater  reluctance  will  be  produced  in  the  circuit. 

(2.)  A  leakage  or  shunt  path  will  now  be  formed  through  the 
air  between  the  poles  TV^and  S.  Strictly  speaking,  there  will  be 
some  leakage  in  the  preceding  case  of  Fig.  48,  but  with  a  ferric 
circuit  of  comparatively  short  length,  it  will  have  been  so  small 
as  to  be  practically  negligible.  In  Fig.  49,  however,  the  reluc- 
tance of  the  main  circuit  between  the  poles  including  the  air- 
gaps  will  be  so  great  as  to  give  rise  to  a  considerable  difference 
of  magnetic  potential  between  the  poles  N and  S,  so  that  appre- 
ciable leakage  will  occur  between  these  points.  The  reluctance 
of  the  leakage-paths  through  the  air  will  usually  be  very  com- 
plex, and  difficult  to  compute,  but,  in  simple  geometrical  cases, 
it  may  be  approximately  obtained  without  great  difficulty.  In 
this  case  we  may  proceed  to  determine  the  magnetic  circuit 
first  on  the  assumption  that  no  leakage  exists,  and  second  on 
the  assumption  of  the  existence  of  a  known  amount  of  leakage. 
Assuming  that  the  cores  are  of  soft  Norway  iron,  and  that 
it  is  required  to  establish  a  total  flux  of  204,000  webers 
through  the  circuit,  then  the  flux  density  in  the  iron  will  be  17 
kilogausses  and  its  reluctivity  0.0073.  The  reluctance  of  the 
circuit,  so  far  as  it  is  composed  of  iron,  will  be  0.03042  oersted, 

I    27 

while  the  reluctance  of  each  air-gap  will  be  -— -  X  i  =  0.1058; 

or,  in  all,  0.2016  oersted.  The  total  reluctance  of  the  circuit 
will,  therefore,  be  0.23202  oersted,  and  the  M.  M.  F.  required 
will  be  204,000  x  0.23202  =  47,330  gilberts  =  37,660  ampere- 
turns;  or,  with  2,000  turns,  18.83  amperes.  The  attractive 
force  on  the  armature  will  be  620  Ibs.  as  in  the  previous 
case. 

78.  Considering  now  the  effect  of  leakage,  we  may  assume 
that  the  reluctance  of  the  leakage  path  through  the  air  Jt3,  is 
o.  5  oersted,  and  that  a  flux  of  108  kilowebers  has  to  be  produced 
through  the  lower  core;  the  length  of  mean  path  in  the  lower 
core  being  20  cms.,  and  in  the  upper  core  30  cms.,  it  is  required 
to  find  the  M.  M.  F.,  which  will  produce  this  flux  through  the 
lower  core. 

The  intensity  in  the  lower  core  will  be  -  °  *°c-  =  9,000 
gausses,  at  which  intensity  the  reluctivity  of  Norway  iron  will 


AERO-FERRIC  MAGNETIC  CIRCUITS.  73 

be,  by  Fig.  47,  0.000,6,  so  that  the  reluctance  of  the  lower  core 

will  be  —  X  0.000,6  =  o.ooi  oersted,  and  this  added  to  the  re- 
12 

luctance  of  the  two  air-gaps,  1.27  cms. in  width,  =  0.2016  -f-o.ooi 
=  o.  2026  oersted.  The  magnetic  difference  of  potential  in  this 
branch  of  the  double  circuit  will,  therefore,  be  108,000  x  0.2026 
=  21,880  gilberts.  This  will  also  be  the  difference  of  magnetic 
potential  between  the  terminals  of  the  leakage  path  R^  and  the 

leakage  flux  will,  therefore,  be  — —  43,760  webers.    The 

total  flux  in  the  main  circuit  through  the  upper  core  will  be  the 
sum  of  the  flux  in  the  two  branches,  or  108,000  -}-  43,760  = 

151,760  webers,  making  the  intensity  in  the  upper  core         * — 
=  12,647  gausses,  at  which  intensity  the  reluctivity  is  0.00121, 

so  that  the  reluctance  of  the   upper  core  is  —  X    0.0012   = 

12 

0.003  oersted.  The  drop  of  potential  in  the  upper  core  will, 
therefore,  be  151,760  x  0.003  =  455  gilberts,  and  the  total 
difference  of  potential  in  the  circuit,  or  the  M.  M.  F.,  will  be 
21,880  -|-  455  =  22,335  gilberts  =  17,775  ampere-turns,  or 
8.89  amperes  at  2,000  turns. 

79.  It  is  obvious  that  the  results  obtained  by  the  preceding 
method  of  calculation  cannot  be  strictly  accurate,  since  no 
account  has  been  taken  of  any  magnetic  leakage  except  that 
whicH  occurs  directly  between  the  poles  N  and  S.  Also  we 
have  assumed  that  the  flux  density  remains  uniform  through- 
out the  lengths  of  the  two  cores.  When  a  greater  degree  of 
accuracy  is  desired,  corrections  may  be  introduced  for  the 
effects  of  these  erroneous  assumptions,  but  the  examples  illus- 
trate the  general  methods  by  which  the  magnetic  circuits  of 
practical  dynamo-electric  machines  may  be  computed  with  fair 
limits  of  accuracy. 


CHAPTER  VII. 

LAWS   OF    ELECTRO-DYNAMIC    INDUCTION. 

80.  When  a  conducting  wire  is  moved  through  a  magnetic 
flux,  there  will  always  be  an  E.  M.  F.  induced  in  the  wire, 
unless  the  motion  of  the  wire  coincides  with  the  direction  of 
the  flux;  or,  in  other  words,  unless  the  wire  in  its  motion  does 


FIG.  50. — CONDUCTOR   PERPENDICULAR   TO    UNIFORM    MAGNETIC   FLUX,  AND 
MOVING   AT   RIGHT   ANGLES   TO    SAME. 

not  pass  through  or  cut  the  flux.  Thus,  if,  as  in  Fig.  50,  a 
straight  wire  A  B,  of  /  cms.  length,  extending  across  a  uniform 
flux,  be  moved  at  right  angles  to  the  flux,  either  upwards  or 
downwards,  to  the  position,  for  example,  a  b,  or  a'  b\  it  will 
have  an  E.  M.  F.  induced  in  it,  the  direction  of  which  will 
change  with  the  direction  of  the  motion. 

8l.  A  convenient  rule  for  memorizing  the  direction  of  the 
E.  M.  F.  induced  in  a  wire  cutting,  or  moving  across,  magnetic 
flux,  is  known  as  Fleming's  hand  rule.  Here,  as  in  Fig.  51,  the 
right  hand  being  held,  with  the  thumb,  the  forefinger  and  the 
middle  finger  extended  as  shown,  the  thumb  being  so  pointed 
as  to  indicate  the  direction  of  wotion,  and  the /brefinger  the 
direction  of  the  magnetic /lux,  then  the  middle  finger  will  indi- 
cate the  direction  of  induced  E.  M.  F.  For  example,  if,  as  in 

74 


LAWS  OF  ELECTRO-DYNAMIC  INDUCTION.  75 

Fig.  50,  a  wire  be  moved  vertically  downwards  from  A  B,  to 
a  b ',  and  the  thumb  be  held  in  that  direction,  the  forefinger 
pointing  in  the  direction  of  the  flux,  the  E.  M.  F.  induced  in 
the  wire  will  take  the  direction  a'  £',  during  the  motion,  follow- 
ing the  direction  of  the  middle  finger.  If,  however,  the  wire 
be  moved  upwards  through  the  flux,  an  application  of  the  same 


FIG.   51. — FLEMING  S    HAND   RULE. 

rule  will  show  that  the  direction  of  the  induced  E.  M.  F.,  as 
indicated  by  the  middle  finger,  is  now  changed. 

82.  The  induction  of  electromotive  force  in  a  conductor, 
moving  so  as  to  pass  through  or  cut  magnetic  flux,  is  called 
electro-dynamic  induction.  The  value  of  the  E.  M.  F.  induced  in 
a  wire  by  electro-dynamic  induction  depends, 

(i.)  On«the  density  of  the  magnetic  flux. 

(2.)  On  the  velocity  of  the  motion,  and 

(3.)  On  the  length  of  the  wire. 

This  is  equivalent  to  the  statement  that  the  E.  M.  F.,  in- 
duced in  a  given  length  of  wire,  depends  upon  the  total  amount 


76  ELECTRO-DYNAMIC  MACHINERY. 

of  flux  cut  by  the  wire  per  second  in  the  same  direction;  or, 
e  =  ($>lv  C.  G.  S.  units  of  E.  M.  F. 

Where  (B,  is  the  intensity  of  the  flux  in  gausses,  /,  the  length 
of  the  conductor  in  cms.,  v,  the  velocity  of  motion  in  cms.-per- 
second,  and  ^,  the  induced  electromotive  force  as  measured  in 
C.  G.  S.  units.  Since  one  international  volt  is  equal  to 


FIG.  52. — CONDUCTOR   OBLIQUE   TO    UNIFORM   MAGNETIC   FLUX,  AND 
MOVING   AT   RIGHT   ANGLES   TO    SAME. 

100,000,000  C.  G.  S.  units  of  E.  M.  F.,  the  E.  M.  F.  induced 
in  the  wire  will  be 

e  = •  volts. 

100,000,000 

83.  The  preceding  equation  assumes  that  the  wire  is  not 
only  lying  at  right  angles  to  the  flux,  but  also  that  it  is  moved 
in  a  direction  at  right  angles  to  the  direction  of  the  flux.  If 
instead  of  being  at  right  angles  to  the  flux,  the  wire  makes  an 
angle  /?,  with  the  perpendicular  to  the  same,  as  shown  in  Fig. 
52,  then  the  length  of  the  wire  has  to  be  considered  as  the 
virtual  length  across  the  flux,  or  as  its  projection  on  the 
normal  plane,  so  that  the  formula  becomes, 

(B  /  v  cos  fi 

e  = volts. 

100,000,000 

If  the  motion  of  the  wire,  instead  of  being  directed  perpendic- 
ularly to  the  flux,  is  such  as  to  make  an  angle  a,  with  the  per- 
pendicular plane,  the  effective  velocity  is  that  virtually  taking 


LAWS   OF  ELECTRO-DYNAMIC  INDUCTION.  ^^ 

place  perpendicular  to  the  flux,  or  v  cos  a,  as  shown  in  Fig.  53, 
so  that  the  formula  becomes  in  the  most  general  case, 


e  =  &  l  cos  f  '"  cos  a  volts 

100,000,000 


84.  It  will  be  seen  that  in  all  cases  the  amount  of  flux  cut 
through  uniformly  in  one  second,  gives  the  value  of  the  E.  M.  F: 


FIG.  53. — CONDUCTOR   OBLIQUE   TO    UNIFORM    MAGNETIC    FLUX,    AND 
MOVING   OBLIQUELY   TO    SAME. 

induced  in  the  wire,  and  that  the  value  of  the  E.  M.  F.  does  not 
depend  upon  the  amount  of  flux  that  has  been  cut  through,  or 
that  has  to  be  cut  through,  but  upon  the  instantaneous  rate  of 
cutting.  The  E.  M.  F.  ceases  the  moment  the  cutting  ceases. 

85.  If  the  loop  A  B    C  £>,  Fig.  54,  be   rotated   about  its 
axis  O  O',  in  the  direction  of  the  curved  arrows,  then,  while 
the  side  C  D,  is  ascending,  the  side  A  B,  is  descending;  con- 
sequently, the   E.  M.  F.  in  the  side   C  D,  will   be   oppositely 
directed  to  the  E.  M.  F.  in  the  side  A  B.     Applying  Fleming's 
hand  rule  to  this  case,  we  observe  that  the  directions  of  these 
E.  M.  Fs.  are  as  indicated  by  the   double-headed  arrows,  and, 
regarding  the  conductors  CD  and  A  B,  as  forming  parts  of 
the  complete  circuit  C  D  A  B,  it  is  evident  that  the  E.  M.  Fs. 
induced  in  A  B  and  C  D,  will  aid  each  other,    while,    if  they 
are   permitted   to    produce    a   current,   the   current   will    flow 
through  the  circuit  in  the  same  direction. 

86.  We    have  seen   that  no  E.   M.  F.  is  induced  in  a  wire 
unless  it  cuts  flux.     Consequently,  the  portions  B  C  and  A  D, 
of  the  circuit  which  move  in  the  plane  of  the  flux,  will  con- 
tribute nothing  to  the  E.  M.  F.  of  the  circuit. 


78  ELECTRO-DYNAMIC  MACHINERY. 

If  the  dimensions  of  the  wires  forming  this  loop  shown  in 
the  figure,  are  such  that  C  D  and  A  B,  having  each  a  length 
of  12  cms.,  while  A  B  and  B  C,  are  4  cms.  each.,  the  circumfer- 
ence traced  by  the  wires  A  B  and  C  D,  in  their  revolution 
about  the  axis,  will  be  3.1416  x  4  =  12.567  cms. ;  and,  if  the 
rate  of  rotation  be  50  revolutions  per  second,  the  speed  with 
which  the  wires  A  B  and  C  Z>,  revolve  will  be  628.3  cms.  per 
second.  If  the  intensity  of  the  magnetic  flux  B,  is  uniformly 
5  kilogausses,  the  E.  M.  F.  induced  in  each  of  the  wires  A  B 


FIG.  54. — RECTANGULAR   CONDUCTING   LOOP   ROTATING   IN    UNIFORM 
MAGNETIC   FLUX. 

and  C  D,  will  be,  5,000  x  12  x  628.32=37,699,200  C.  G.  S, 
units  of  E.  M.  F.,  or  0.377  volt.  This  value  of  the  E.  M.  F. 
only  exists  at  the  instant  when  the  loop  has  its  plane  coincident 
with  the  plane  of  the  flux,  and  the  sides  cut  the  flux  at  right 
angles.  In  any  other  position,  the  motion  of  these  sides  is 
not  at  right  angles  to  the  flux,  so  that  the  E.  M.  F.  is  reduced. 

87.  In  order  that  the  E.  M.  F.  induced  in  a  wire  may  estab- 
lish a  current  in  it,  it  is  necessary  that  such  wire  should  form 
a  complete  curcuit  or  loop,  as  indicated  in  Fig.  55.  When 
such  a  conducting  loop  is  moved  in  a  magnetic  field,  some  or 
all  portions  of  the  loop  will  cut  flux,  and  will  thereby  contribute 
a  certain  E.  M.  F.  around  the  loop.  If  the  loop  moves  in  its. 
own  plane,  in  a  uniform  magnetic  flux,  there  will  be  no  resultant 
E.  M.  F.  generated  in  it.  For  example,  considering  a  circular 
loop,  we  may  compare  any  two  diametrically  opposite  segments, 
when  it  is  evident  that  each  member  of  such  a  pair  cuts  through 
the  same  amount  of  flux  per  second,  and  will,  therefore,  gener- 
ate the  same  amount  of  E.  M.  F.,  but  in  directions  opposite 
to  each  other  in  the  loop.  At  the  same  time,  it  is  clear  that 


LAWS   OF  ELECTRO-DYNAMIC  INDUCTION.  79 

the  total  amount  of  flux  in  the  loop  does  not  change;  for, 
while  the  flux  is  being  left  by  the  loop  at  its  receding  edge,  it 
is  entering  the  loop  at  the  same  rate  at  its  advancing  edge,  and, 
since  these  two  quantities  of  flux  are  equal,  the  total  amount 
of  flux  enclosed  by  the  loop  remains  constant. 

88.  The  cutting  of  flux  by  the  edges  of  a  moving  loop,  there- 
fore, resolves  itself  into  the  more  general  condition  of  enclos- 
ing flux  in  a  loop.  The  value  of  the  E.  M.  F.  induced  around 


FIG.  55. — CIRCULAR   CONDUCTING   LOOP    PERPENDICULAR   TO    UNIFORM 
MAGNETIC   FLUX. 

the  loop  does  not  depend  upon  the  actual  quantity  of  flux 
enclosed,  but  on  the  rate  at  which  the  enclosure  is  being 
made.  If,  as  we  have  already  seen,  the  loop  is  so  moved 
that  the  total  flux  it  encloses  undergoes  no  variation,  the 
amount  entering  the  loop  being  balanced  by  the  amount  leav- 
ing it,  although  E.  M.  Fs.  will  be  induced  in  those  parts  of 
the  loop  where  the  flux  is  entering  and  where  it  is  leaving,  yet 
these  E.  M.  Fs.  being  opposite,  exactly  neutralize  each  other, 
and  leave  no  resultant  E.  M.  F.  Consequently,  the  value  or" 
the  E.  M.  F.  induced  at  any  moment  in  the  loop  by  any 
motion,  does  not  depend  upon  the  flux  density  within  the  loop, 
but  on  the  rate  of  change  of  flux  enclosed. 

89.  If  $,  be  the  total  flux  in  webers  contained  within  a 
single  loop,  such  as  shown  at  A  B  C,  in  Fig.  55,  the  mean  rate 
at  which  this  flux  is  changing  during  any  given  period  of  time, 
will  be  the  quotient  of  the  change  in  the  enclosure,  divided  by 


So  ELECTRO-DYNAMIC  MACHINERY. 

that  amount  of  time,  so  that  if  $,  changes  by  20,000  webers  in 
two  seconds,  the  mean  rate  of  change  during  that  time  will  be 
10,000  webers  per  second,  and  this  will  be  the  E.  M.  F.  in  the 
loop  expressed  in  C.  G.  S.  units.  But,  during  these  two  seconds 
of  time,  the  change  may  not  have  been  progressing  uniformly, 
in  which  case  only  the  average  E.  M.  F.  can  be  stated  as  being 
equal  to  the  10,000  C.  G.  S.  units.  Where  the  change  is  not 
uniform,  the  rate  at  any  moment  has  to  be  determined  by 
taking  an  extremely  short  interval,  so  that  if  dt,  represents 


$2s> 

&£.>•£•-  x^ 

tiiiti 


FIG.  55A. — RECTANGULAR   CONDUCTING   LOOP   IN   NON-UNIFORM 
MAGNETIC   FLUX. 

this  indefinitely  small  interval  of  time,  and  d$,  the  correspond- 
ing change  in  the  flux  enclosed  during  that  interval  in  webers, 

d <!> 
the  rate  of  change  will  be  — — webers-per-second,  and  this  will 

be  the  value  of  the  induced  E.  M.  F.  at  each  instant. 

90.  If  a  small  square  loop  of  wire  A  B  C  Z>,  one  cm.  in 
length  of  edge,  placed  at  right  angles  to  the  flux  as  shown  in 
Fig.  55  A,  contains  a  total  quantity  of  flux  amounting  to  10,000 
webers,  the  mean  flux  density  at  the  position  occupied  by  the 
square,  will  be  10,000  gausses.  If  now,  the  loop  be  moved 
uniformly  upward  in  its  own  plane  to  the  position  a  bed,  so 

as  to  accomplish  the  journey   in  the  — th  part  of  a  second, 

and  if  the  flux  enclosed  by  the  loop  at  the  position  a  bed, 
be  1,000  webers,  then  9,000  webers  will  have  escaped  from  the 
loop  during  the  motion.  Assuming  that  the  distribution  of 
flux  density  in  the  field  was  such  that  the  emission  took 


LAWS  OF  ELECTRO-DYNAMIC  INDUCTION.  81 

place  uniformly,  the  E.  M.  F.  in  the  loop,  during  the  passage, 
will  have  been, 

— j—  =    - —  —  —  900,000  C.  G.  S.   units  —  0.009  volt. 
A*  rro 

91.  If,   however,   the  rate  of  emptying,  during  the  motion, 
were  not  uniform,  0.009  vo^  would  be  the  average  E.  M.  F., 
and  not  the  E.   M.   F.   sustained   during  the  interval;   or,   in 
other  words,  the  instantaneous  value  of  the  E.  M.  F.   in  the 
loop  would  vary  at  different  portions  of  this  short  interval  of 
time,  or  at  corresponding  different  positions  during  the  jour- 
ney ;  but,  in  all  cases,  the  time  integral  of  the  E.  M.  F.  will 
be  equal  to  the  change  in  £> ;  thus,  the  change  in  <&,  is,  in  this 

case,   9,000   webers.     If   the   motion   is   made   in   — th  of  a 

100 

second,  the  E.  M.  F.,  will  be  900,000  C.  G.  S.  units  of  E.  M.  F., 
which,  multiplied  by  the  time  (o.oi  second),  gives  9,000  webers. 
If,  however,  the  motion  were  uniformly  made  in  half  a  second, 
the  E.  M.  F.  would  have  been  18,000  C.  G.  S.  units,  which, 
multiplied  by  the  time,  would  give  as  before  9,000  webers; 
and  under  whatever  circumstances  of  velocity  the  change  were 
made,  the  sum  of  the  products  of  the  instantaneous  values  of 
E.  M.  F.  multiplied  into  the  intervals  of  time  during  which 
they  existed,  would  give  the  total  change  in  flux  of  9,000 
webers.  Or  in  symbols, 

c.  d<f> 

Since  e  —  --=-- 
at 

fe  dt  =  A  $> 

The  first  equation  simply  expresses  that  the  E.  M.  F.,  ^,  is 
the  instantaneous  rate  of  change  in  the  flux  enclosed,  and  the 
second  equation  shows  that  the  difference  in  the  enclosure 
between  any  two  conditions  of  the  loop  is  the  time  integral  of 
the  E.  M.  F.,  which  has  been  induced  in  the  loop  during  the 
change,  assuming  of  course,  that  the  change  continues  in  the 
same  direction  ;  i.  e. ,  that  the  flux  through  the  loop  has  con- 
tinually increased  or  decreased. 

92.  If  a  circuit  contains  more  than  one  loop,  as,  for  example, 
when  composed  in  whole,   or  in  part,  of  a  coil,  the   turns  of 
which  are  all  in  series,  the  E.  M.  F.  induced  in  any  one  turn 


82  ELECTRO-DYNAMIC  MACHINERY. 

or  loop  of  the  coil,  may  be  regarded  as  being  established  inde- 
pendently of  all  the  other  loops,  so  that  the  total  E.  M.  F.  in 
the  circuit  will  be  the  sum  of  all  the  separate  E.  M.  Fs.  exist- 
ing at  any  instant  in  the  loops,  and  may,  therefore,  be  regarded 
as  the  instantaneous  rate  of  change  in  the  flux  linked  with  the 
entire  circuit.  A  coil,  therefore,  may  be  regarded  as  a  device 
for  increasing  the  amount  of  flux  magnetically  linked  with  an 
electric  circuit,  so  that  by  increasing  the  number  of  loops  of 
conductor  in  the  circuit,  the  value  of  the  induced  E.  M.  F. 
corresponding  to  any  change  in  the  flux,  is  proportionally 
increased,  and  if  the  coil  or  system  of  loops  forming  the.  cir- 


c 
FIG.   56.— CLOSED    CIRCULAR    HELIX   LINKED   WITH   A   LOOP   OF  WIRE. 

cuit,  contains  in  the  aggregate  $  webers  of  flux  linked  with  it, 
taking  each  turn  separately  and  summing  the  enclosures,  then 
the  time  integral  of  E.  M.  F.  in  the  circuit  will  be  the  total 
change  in  $>,  and  this  will  be  true,  whether  the  loop  is  chang- 
ing its  position,  or  whether  the  flux  is  changing  in  intensity  or 
in  direction. 

93.  It  is  evident  from  the  preceding,  that  there  are  two 
different  standpoints  from  which  we  may  regard  the  produc- 
tion of  electromotive  force  in  a  conducting  circuit  by  electro- 
dynamic  induction  ;  namely,  that  of  cutting  magnetic  flux,  and 
that  of  enclosing  magnetic  flux.  These  two  conceptions  are 
equivalent,  being  but  different  ways  of  regarding  the  same 
phenomenon.  The  amount  of  flux  enclosed  by  a  loop  can 
only  vary  by  the  flux  being  cut  at  the  entering  edge  or  edges 
at  a  different  rate  to  that  at  the  receding  edge;  or,  in  mathe- 
matical language,  the  surface  integral  of  enclosing  is  equal  to 


LAWS  OF  ELECTRO-DYNAMIC  INDUCTION.  83 

the  line  integral  of  cutting,  taken  once  round  the  loop.  This 
statement  is  equally  true  whether  the  flux  is  at  rest  and  the 
conductor  moving,  or  the  conductor  at  rest  and  the  flux  mov- 
ing, or  whether  both  conductor  and  flux  are  in  relative  motion. 

94.  Cases  of  electro-dynamic  induction  may  occur  where  the 
equivalence  of  cutting  and  enclosing  magnetic  flux  apparently 
fails.  On  closer  examination,  however,  the  equivalence  will  be 
manifest.  For  example,  in  Fig.  56,  let  A  B  C  D  be  a  wooden 
anchor  ring  uniformly  wound  with  wire,  as  shown  in  Fig.  44, 
and  a  b  c  d,  a  circular  loop  of  conductor  linked  with  the  ring. 


FIG.   57. — SQUARE    CONDUCTING   LOOP   ROTATED   IN    UNIFORM    FLUX. 
FIRST   POSITION. 

It  has  been  experimentally  observed  that  when  a  powerful  cur- 
rent is  sent  through  the  winding  of  the  anchor  ring,  no  appreci- 
able magnetic  flux  is  to  be  found  at  any  point  outside  the  ring, 
although  within  the  core  of  the  ring  a  powerful  magnetic  flux 
is  developed.  Nevertheless,  both  at  the  moment  of  applying 
and  at  the  moment  of  removing  the  exciting  current  through 
the  winding  of  the  ring,  an  E.  M.  F.  is  induced  in  the  loop 
a  b  c  d,  whose  time  integral  in  C.  G.  S.  units,  is  the  total 
number  of  webers  of  change  of  flux  in  the  ring  core.  It  might 
appear  at  first  sight  that  this  E.  M.  F.  so  induced  in  the  loop 
cannot  be  due  to  the  cutting  of  flux  by  the  loop,  but  must  be 
due  to  simple  threading  or  enclosing  of  flux.  It  is  clear,  how- 
ever, that  the  mere  act  of  enclosure  will  not  account  for  the 
induction  of  the  E.  M.  -F.,  since  the  passage  of  flux  through 
the  centre  of  the  loop  cannot  produce  E.  M.  F.  in  the  loop 
itself,  unless  activity  is  transmitted  from  the  centre  of  the  loop 


84  ELECTRO-DYNAMIC  MACHINERY. 

to  its  periphery.  In  other  words,  action  at  a  distance,  with- 
out intervening  mechanism  of  propagation,  is  believed  to  be 
impossible. 

Could  we  see  the  action  which  occurs  when  the  current  first 
passes  through  the  ring-winding,  we  should  observe  flux 
apparently  issuing  from  all  parts  of  the  ring  and  passing  into 
surrounding  space,  at  a  definite  speed.  The  loop  a  b  c  d, 
would  receive  the  impact  of  flux  from  the  adjacent  portions  of 
the  ring  before  receiving  that  from  the  more  distant  parts  of 
the  ring,  and,  in  this  sense,  would  actually  be  cut  by  the  flux. 
As  soon  as  the  flux  has  become  established,  and  the  current  in 


•x      ^ 

S*    ivr      *-- 


+»* 

_* 

>> 


FIG.   58. — SQUARE   CONDUCTING   LOOP   ROTATED   IN   UNIFORM    FLUX. 
SECOND   POSITION. 

the  winding  steady,  it  is  found  that  the  flux  from  any  particu- 
lar portion  of  the  ring  is  equal  and  opposite  to  that  from  the 
remainder  of  the  ring,  and  is,  therefore,  cancelled  or  annulled 
at  all  points  except  within  the  ring  core.  It  is  evident,  there- 
fore, that  we  may  regard  the  E.  M.  F  induced  in  the  loop 
a  b  c  d  as  due  either  to  the  cutting  of  the  boundary  by  flux,  or 
to  the  enclosure  of  flux. 

95.  Let  us  consider  the  case  of  a  square  conducting  loop 
A  B  C  D,  Fig.  57,  having  its  plane  parallel  with  the  uniform 
magnetic  flux  shown  by  the  dotted  arrows.  If  this  loop  be 
rotated  about  the  axis  O  O',  which  is  at  right  angles  to  the 
magnetic  flux,  and  symmetrically  placed  with  regard  to  the 
loop,  so  that  A  D,  descends,  and  B  C,  ascends,  these  sides, 
which  cut  flux  during  the  rotation,  will  have  E.  M.  Fs.  gene- 
rated in  them,  in  accordance  with  Fleming's  hand  rule  already 


LAWS  OF  ELECTRO-DYNAMIC  INDUCTION.  85 

described  in  Par.  81,  and  in  the  direction  shown  by  the 
double  arrows.  The  sides  A  B  and  D  C,  which  do  not  cut  ftux 
during  the  motion,  will  add  nothing  to  the  E.  M.  F.  generated. 
The  figure  shows  that  while  the  sides  AD  and  C B,  have  oppo- 
sitely directed  E.  M.  Fs.,  yet  regarding  the  entire  loop  as  a 
conducting  circuit,  these  E.  M.  Fs.  tend  to  produce  a  current 
which  circulates  in  the  same  direction. 

96.  As  already  pointed  out,  the  value  of  the  E.  M.  F.  gene- 
rated in  the  sides  A  D  and  C  B,  of  the  loop,  by  the  cutting  of 
the  ftux,  will  depend  upon  the  rate  of  filling  and  emptying  the 


FIG.  59. — SQUARE   CONDUCTING  LOOP   ROTATED   IN   UNIFORM   FLUX. 
THIRD   POSITION. 

loop  with  flux,  and  it  is  evident  that  this  rate  is  at  a  maximum 
when  the  loop  is  empty;  /.  <?.,  in  the  position  it  occupies  in 
Fig.  57,  when  the  plane  of  the  loop  coincides  with  the  direc- 
tion of  the  flux,  and  the  motion  of  its  sides  is  at  right  angles 
thereto;  for,  when  the  loop  reaches  the  position  shown  in  Fig. 
58,  namely,  when  it  is  full  of  flux;  or,  when  its  plane  is  as 
right  angles  to  the  flux,  then  at  that  instant  the  rotation  of 
the  loop  neither  adds  to  nor  diminishes,  the  amount  of  flux 
enclosed,  so  that  the  E.  M.  F.  in  the  loop  is  zero. 

97.  Continuing  the  rotation  of  the  loop  in  the  same  direc- 
tion, the  E.  M.  F.  generated  will  increase  from  this  position 
until  the  position  shown  in  Fig.  59  is  reached,  where  the  plane 
of  the  loop  is  again  coincident  with  the  plane  of  the  flux,  but 
in  which  the  side  A  D,  has  moved  through  180°,  or  one-half 
a  revolution  from  the  position  shown  in  Fig.  57,  and  the  direc- 
tions of  E.  M.  Fs.  in  the  wire,  as  shown,  will  be  changed  so  far 


86 


ELECTRO-DYNAMIC  MACHINERY. 


as  the  wire  is  concerned,  being  now  from  A  to  Z>,  instead  of 
from  D  to  A,  in  the  conducting  branch  A  Dj  and  from  C  to  B, 
instead  of  from  B  to  C,  in  the  conducting  branch  B  C.  The 
direction  of  E.  M.  F..  around  the  loop,  will,  therefore,  be 


FIG.  60. — SQUARE   CONDUCTING  LOOP  ROTATED   IN   UNIFORM   FLUX. 
FOURTH    POSITION. 


reversed.  Consequently,  the  loop  A  B  C  D,  during  its  first 
half  revolution  as  shown  in  Figs.  57  to  59,  has  an  E.  M.  F.  in  it 
in  the  same  direction;  and,  during  the  remaining  half-revolu- 
tion, has  its  E.  M.  F.  in  the  reverse  direction,  as  shown. 


S?CL  JK 

»-*.->.-•.  -»..»•-»•  .+•  *^  A*-.*.  •>.  -»  •*-!*-•. 


FIG.  6l. — FLUX   OBLIQUE   TO   PLANE   OF   ROTATING   LOOP. 

98.  The  value  of  the  E.  M.  F.  generated  in  a  loop,  during 
its  rotation,  depends  upon  the  flux  density,  on  the  area  of  the 
loop,  and  on  the  rate  of  rotation. 

Assuming  the  side  of  the  loop  C  Z>,  to  occupy  the  position 
shown  in  Fig.  61,  making  an  angle  a,  with  the  direction  H K,  of 
the  flux,  then  the  E.  M.  F.  generated  in  the  loop  at  this  instant 
is  the  rate  at  which  flux  is  being  admitted  into  the  loop.  If 
/cms.,  be  the  length  of  the  side  of  the  loop  or  the  length  of 
A  Z>,  in  Fig.  57,  the  amount  of  flux  embraced  at  this  instant 
will  be  /  ($>  X  2  D  K.  During  the  next  succeeding  small  interval 


LAWS   OF  ELECTRO-DYNAMIC  INDUCTION.  87 

of  time  dt,  if  the  angular  velocity  of  the  loop,  GO  radians  per 
second,  carries  it  to  the  position  C '  D ',  the  amount  of  flux 
admitted  during  that  time  will  be  /  (B  X  2  D  L.  But  D  L  = 
D  D'  X  cosine  of  angle  D' D  L,  and  this  angle  is  equal  to  the 


FIG.  62.— FLUX   COINCIDENT   WITH    PLANE   OF    ROTATING   LOOP. 

angle  <*,  so  that  D  L  —D  D'  xcos  a,  and  D  D',  will  be  — oodt 

cms.  in  length,  since  the  radius  O  D  =  —  ;  consequently,  the 

flux  admitted  into  the  loop  during  this  brief  interval  of  time 
dt,  will  be 

</  $  =  2  /  X  —  ($>  GO  cos  a  dt,  or  /2  (&  GO  cos  a  dt 

=  <&  GO  cos  a  dt 

d  <& 
so  that  —7-    =  $  GO  cos  a. 

at 

Thus,   at  the  instant  of  time  in  which  the  loop  has  reached  the 

D    D 


H  **•*•  -»-- 


cuc/ 

FIG.  63. — FLUX  PERPENDICULAR  TO  PLANE  OF  ROTATING  LOOP. 

position  O  D,  if  «,  be  the  angle  which  the  loop  makes  at  any 
time  with  the  direction  of  the  flux,  the  E.  M.  F.  <?,  the  instan- 
taneous rate  of  increase  in  the  flux,  or  will  be  generally  ex- 
pressed in  C.  G.  S.  units  by 

e  =  0  GO  cos  a 
$,  being  the  maximum  amount  of  flux  in  webers  (/2  (B),  which 


88 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


the  loop  can  embrace.  When  the  plane  of  the  loop  coincides 
with  the  direction  H  K,  of  the  flux,  as  shown  in  Fig.  62,  D  D'9 
is  brought  into  coincidence  with  D  Lf  or  the  cosine  of  a  is  i. 
So  that  the  E.  M.  F.  ^,  in  the  loop  has  a  maximum  value,  and 


1 

0.51 


-0.5; 
-1 


FIG.  64. — CURVE  OF  E.  M.  F.  INDUCED  IN  ROTATING  LOOP. 

is  equal  to  $  a>,  while  when  the  loop  is  at  right  angles  to  the 
flux,  or  as   shown   in   Figure  63,   D  D',  the   succeeding  small 


FIG.  65. — CURVE   OF   E.   M.  F.   INDUCED    IN    LOOP    ROTATING 
AT    DOUBLED    SPEED. 

excursion  of  the  loop,  is  at  right  angles  to  D  Z,  or  cosine  a  =  o, 
so  that  e  —  o. 


99.  If  (B,  as  in  the  case  represented  by  Figs.  57  to  60,  be  twa 
kilogausses,  and  /  =  100  cms.,  then  $  =  100  x  100  X  2,000  =  20- 


LAWS  OF  ELECTRO-DYNAMIC  INDUCTION.  89 

megawebers.     If  the  loop  be  rotated  in  the  direction  shown  at 
an  angular  velocity  of  50  radians  per  second  (  --  revolutions 

per  second),  the  E.  M.  F.  ^.,  will  be 

e  =  20,000,000  X  50  X  cos  a,  or  100,000,000  cos  a 

=  i  cos  a     volt. 

The   E.   M.    F.    generated   by   the   loop,    therefore,    varies 
periodically  between  i,  o,  —  i,  o,  and  i.     If  these  values  be 


0.5- 

g 
I 


1! 


FIG.  66. — CURVE   OF   E.  M.  F.  COMMUTED   IN   EXTERNAL    CIRCUIT. 

plotted  graphically  as  ordinates,  to  a  scale  of  time  as  abscissas, 
the  curve  shown  in  Fig.  64  will  be  obtained,  where  the  distance 
A  O,  represents  the  time  occupied  by  one  half  revolution  of  the 
loop,  the  E.  M.  F.  being  positive  from  O  to  A,  and  negative 
from  A  to  B.  If  now,  the  speed  of  revolution  be  doubled; 
i.  e.,  increased  to  TOO  radians  per  second,  the  time  occupied  in 
each  revolution  will  be  halved,  and  O'A',  Fig.  65,  will  be  half 
the  length  of  O  A,  but  e,  will  be  doubled  as  shown.  The 
shaded  area  O'  C'  A',  in  Fig.  65,  is  equal  to  the  area  O  C  A,  of 
of  Fig.  64.  The  E.  M.  F.  generated  by  the  loop  is  alternating, 
being  positive  and  negative  during  successive  half  revolutions, 
but,  by  the  aid  of  a  suitable  commutator,  the  E.  M.  F.  can  be 
made  unidirectional  in  the  external  circuit,  as  represented 
in  Fig.  66,  where  the  curve  P  S  Q,  corresponds  to  OCA,  in 
Fig.  64  and  Q  T  R,  to  A  D  B. 


CHAPTER   VIII. 

ELECTRO-DYNAMIC    INDUCTION    IN    DYNAMO    ARMATURES. 

100.  The  type  of  curve  represented  in  Figs.  64,  65,  and  66, 
showing  the  E.  M.  F.  generated  by  the  rotation  of  a  conduct- 
ing loop  in  a  uniform  magnetic  flux,  may  be  produced  by  the 
rotation  of  the  coil  represented  in  Fig.  67.  Here  a  number  of 
circular  loops,  formed  by  winding  a  long  insulated  wire  upon 


FIG.  67. — COIL  FOR  INDUCING  FEEBLE  E.  M.  FS.  BY  REVOLUTION 
IN  EARTH'S  MAGNETIC  FLUX. 

a  circular  wooden  frame,  are  capable  of  being  rotated  by  the 
handle,  in  the  uniform  magnetic  flux  of  the  earth.  If  the 
mean  area  of  the  loops  be  1,000  sq.  cms.,  the  number  of  loops 
500,  and  the  intensity  of  the  earth's  magnetic  flux  threading 
the  loop  0.6  gauss,  then  the  E.  M.  F.  generated  by  rotating  the 
loop  will  depend  only  on  the  speed  of  rotation.  Assuming  this 
to  be  5  revolutions-per-second,  or  an  angular  velocity  of 
5  x  2  n  —  15.708  radians-per-second,  the  E.  M.  F.  will  vary 
between  -\-  3>  GO  and  — £>  &?,  in  each  half  revolution.  Here  $, 
the  total  flux  linked  with  the  coil  is  500  X  1,000  X  0.6  —  300,000 


INDUCTION  IN  DYNAMO  ARMATURES.  91 

webers,  and  GO  —  15.708,  so  that  the  maximum  value  of  the 
E.   M.    F.    generated   in  the   coil   will  be  4,712,400   C.    G.    S 

units  —  0.047  volt,  or  roughly  — th  volt.     This    corresponds 

to  the  peaks  C  and  £>,  of  the  waves  of  induced  E.  M.  F.  shown 
in  Fig.  64. 

101.  In  practice,  however,  continuous-current  generators 
do  not  produce  this  type  of  E.  M.  F.  Fig.  68  represents,  in 
cross-section,  a  common  type  of  generator  armature,  situated 
between  two  field  poles  JV,  and  S.  A  type  of  generator, 
armature  and  field  poles,  similar  to  this,  is  seen  in  Fig.  i. 

The  flux  from  these  poles  passes  readily  into  and  out  of  the 
armature  surface  as  indicated  by  the  arrows.  In  other  words, 


FIG.  68. — CROSS-SECTION   OF   BIPOLAR   DRUM   ARMATURE. 

the  flux  cuts  the  surface  of  the  armature  at  right  angles,  while, 
in  the  cases  shown  in  Figs.  57  to  60,  the  conducting  loop  is 
only  cut  by  the  flux  at  right  angles  in  two  positions  180°  apart, 
so  that  the  curve  of  E.  M.  F.  is  peaked  at  these  points,  and 
descends  rapidly  from  them  on  each  side. 

102.  Suppose  in  Fig.  68  that  the  difference  of  magnetic 
potential,  maintained  between  .Wand  S,  is  2,000  gilberts,  that 
the  diameter  of  the  armature  core  g  o  h,  is  40  cms.,  that  its 
length  is  100  cms.,  and  that  the  air-gap  or  entrefer  is  i  cm.; 
then,  if  the  reluctance  of  the  iron  armature  core  be  regarded 
as  negligibly  small,  the  magnetic  potential  between  the  polar 
surfaces  and  the  armature  surface  on  each  side,  that  is  between 
c  N  e  and  A  g  B,  also  between  d  S  f  and  A  h  B,  will  be  1,000 
gilberts.  The  magnetic  intensity  in  the  air  may  be  obtained 
in  two  ways. 

(i.)  By  considering  the  total  reluctance  of  the  air-gap  and 
obtaining,  by  this  means,  the  total  flux.  Thus  the  polar  surface 
represented  is  55  cms.  in  arc  x  100  cms.  in  breadth  =  5,500 


92  ELECTRO-DYNAMIC  MACHINERY. 

sq.  cms.     The  reluctance  of  the  air-gap  on  either  side  of  the 

armature  is,  therefore,  —  —  oersted,  and  the  total  flux  passing 
5>5°° 

£F       1,000 
through  the  air  will,  therefore,  be  $  =  —  =    -y-    =  5,500,000 


webers.    This  flux,  divided  by  the  area  through  which  it  passes, 

gives  the  intensity,  or  5o00>000  __  Ij000  gausses. 

5>5°° 

(2.)  The  magnetic  intensity  is,  as  we  have  seen  (Par.  53), 
numerically  equal  to  the  drop  of  magnetic  potential  in  air,  or 
other  non-magnetic  material,  per  centimetre,  so  that  the  drop 


1000- 


-flwo- 


t   1 

DEGREES  OF  ANGULAR 

DEVIATION     FROM 
VERTICALRAPI'JSOA. 


FIG.  69. — DIAGRAM   OF   MAGNETIC   INTENSITY    IN    AIR-GAP. 

of  potential  being  here  1,000  gilberts  in  i  cm.  of  distance  in  air, 
the  intensity  must  be  1,000  gausses.  Representing  the  in- 
tensity graphically,  as  shown  in  Fig.  69,  it  will  be  seen  that 
the  intensity  is  uniform  from  c  to  <?,  Fig.  68,  and  then  descends 
rapidly  to  zero  at  B,  where  it  changes  sign  and  becomes 
negatively  directed,  and  is  then  uniform  from  f  to  d,  falling 
again  to  zero  at  A.  The  flux  direction,  therefore,  changes 
sign  twice  in  each  revolution. 

103.  If  a  wire  A  B,  be  wound  as  a  loop  around  the  armature, 
it  will,  when  the  armature  revolves,  cut  this  flux  at  right 
angles,  and  will,  therefore,  have  induced  in  it  an  E.  M.  F. 
which  must  be  of  the  same  type  graphically  as  the  curve  in 
Fig.  69.  Thus,  if  the  surface  of  the  armature  moves  at  a  rate 
of  50  cms.  per  second,  the  E.  M.  F.  induced  in  the  loop  will 
be  2  v  I  (B,  the  factor  2  being  required,  since  both  sides  of 
the  loop  are  cutting  flux,  one  at  A,  and  the  other  at  B;  or, 
2  X  50  X  TOO  X  1,000  =  10,000,000  C.  G.  S.  units  =  o.  i  volt. 


INDUCTION  IN  DYNAMO   ARMATURES. 


93 


except  at  the  moment  when  the  wires  emerge  from  beneath 
the  pole  pieces.  This  curve  is  represented  in  Fig.  70,  where 
the  distance  O  F,  represents  the  time  of  one  complete  revolu- 
tion of  the  armature,  and  the  elevation  of  A,  corresponds  to 
o.i  volt.  If  the  armature  be  set  revolving  at  twice  this 
speed,  the  time  occupied  in  a  revolution  will  be  halved,  but  the 
E.  M.  F.  being  proportional  to  the  rate  of  cutting  flux,  will 


Iff 


FIG.   70. — DIAGRAM   OF    INDUCED   E.  M.  F.  IN   ARMATURE   TURN. 

be  doubled,  as  represented  in  Fig.  71,  where  the  E.  M.  F. 
is  alternately  0.2  volt  in  each  direction.  By  the  aid  of 
a  suitably  adjusted  commutator,  the  E.  M.  F.  instead  of 
changing  sign,  can  be  kept  unidirectional  in  an  external  cir- 
cuit, following  the  curve  o  a  b  c  k  I  fg  hj. 

104.  We  may  regard  the  E.  M.  F.  of  the  loop  as  being  in- 
duced either  by  the  cutting  of  the  flux  by  the  wire  at  the  arma- 


FIG.   71. — DIAGRAM   OF   INDUCED    E.  M.  F.  IN    ARMATURE   TURN 
AT   DOUBLED    SPEED   OF   ROTATION. 


ture  surface,  or  by  the  enclosure  of  the  flux  by  the  loop.  The 
flux  enclosed  by  the  loop  is  represented  by  Fig.  72,  where  at 
the  initial  position  at  A  B,  the  loop  encloses  5,500,000  webers. 
As  the  armature  is  rotated  counter-clockwise,  so  that  A,  is 
carried  toward  7V,  the  flux  enclosed  by  the  loop  diminishes, 
until,  when  it  reaches  the  horizontal  position,  the  flux  through 
the  loop  is  zero.  As  the  rotation  continues,  the  flux  re-enters 
the  loop  in  the  opposite  direction,  and  becomes  5.5  mega- 


94 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


webers  at  a  position  180°  distant  from  the  initial  position^  B. 
The  rate  of  change  of  flux  enclosed,  or  the  gradient  of  the 
curve,  shown  in  Fig.  72,  is  uniform,  since  the  curve  is  uni- 
formly steep,  except  near  the  position  of  maximum  flux,  where 
the  gradient  is  considerably  reduced,  and  the  E.  M.  F.  cor- 
respondingly reduced  as  already  observed  in  Figs.  70  and  71. 


s  X1 
I 


FIG.   72. — REPRESENTING   DIAGRAM    OF    FLUX   ENCLOSED    BY    LOOP 
OF   ARMATURE. 

105.  When,  however,  the  wire  instead  of  being  on  the  sur- 
face of  the  armature  is  buried  in  a  groove  in  the  iron,  as  in  a 
toothed-core  armature  (Par.  22),  and  as  shown  in  Fig.  73, 
it  is  often  mpre  convenient,  for  purposes  of  calculation,  to  con- 
sider the  E.  M.  F.  as  due  to  enclosing,  rather  than  to  cutting 
flux.  The  following  rule,  will,  therefore,  be  of  assistance  in 


FIG.   73. — ARMATURE   LOOP    ROTATING   IN   BIPOLAR    FIELD. 

determining  the  direction  of  the  E.  M.  F.  induced  in  a  loop. 
Bearing  in  mind  the  fact  that  a  watch  dial  is  visible,  to  an  ob- 
server who  holds  it  facing  him,  by  the  light  which  proceeds  in 
straight  lines  from  the  watch  to  his  eye,  then  the  direction  of 
the  E.  M.  F.  induced  in  the  loop,  regarded  as  the  outline  of 
the  watch  face,  can  be  remembered  by  the  following  rule. 


INDUCTION  IN  DYNAMO  ARMATURES. 


95 


The  E.  M.  F.  induced  in  the  loop  has  the  same  direction  as  the 
motion  of  the  hands  of  the  watch,  when  the  flux  entering  the  loop 
has  the  same  direction  as  the  light. 

106.  Flux  entering  the  loop  in  the  opposite  direction,  or  from 
the  observer,  will  induce  an  E.  M.  F.  in  the  opposite  direction  to 
the  hands  of  the  watch,  that  is,  counter-clockwise. 

Emptying  a  loop  of  flux  produces  in  it  an  E.  M.  F.  in  the 
opposite  direction  to  that  produced  by  filling  it. 


FIG.  74. — DIAGRAMS   OF  E.  M.  F. 

107.  Fig.  68,  shows  a  single  loop  of  wire  wound  upon  a  drum 
armature,  which  by  its  rotation  in  the  flux,  has  an  E.  M.  F. 
induced  in  it  of  the  same  type  as  is  graphically  repre- 
sented in  the  curve  of  Fig.  69.  Supposing  that  the  speed  of 
revolution  is  such  as  to  produce  an  E.  M.  F.  of  say  one  volt, 
in  this  conducting  loop,  during  its  passage  beneath  the  pole 
faces,  then  if  two  turns  of  wire  be  wound  on  the  armature  at 
right  angles,  as  shown  at  A  B  and  CD,  Fig.  75,  they  will  each 
generate  E.  M.  F.  of  the  same  value,  in  their  proper  order,  as 
they  pass  through  the  flux,  and  if  the  E.  M.  F.  from  A  B,  is 
represented  by  the  curve  of  a  b  c  d  e  f  g,  of  Fig.  74  A,  and  the 
E.  M.  F.  in  the  loop  CD,  be  represented  simultaneously  by  the 


9°  ELECTRO-DYNAMIC  MACHINERY. 

curve  of  h  i  j  k  I  m  n  <?,  of  Fig.  74  B,  then,  by  properly  adding 
and  co-directing  the .  E.  M.  Fs.  so  produced,  by  the  aid  of  a 
suitable  commutator,  we  obtain  an  E.  M.  F.  of  two  volts,  as 
shown  in  Fig.  75,  C,  by  the  curve  pqrstuvwxyzz'  z". 
Moreover,  while  the  E.  M.  F.  produced  from  one  wire  alone 


FIG.   75. — DRUM    ARMATURE    WOUND    WITH    TWO    TURNS    OF    WIRE   AT    RIGHT 
ANGLES    TO   EACH    OTHER. 

fluctuates  between  o  and  i  volt,  four  times  per  revolution,  the 
E.  M.  F.  produced  by  the  combination  fluctuates  between  i 
and  2  volts-,  eight  times  per  revolution. 

I08.   If  now,  instead  of  two  loops  being  wound  on  the  arma- 
ture, there  are  six  loops,  as  shown  in  Fig.  76,  the  E.  M.  F. 


FIG.     76. — DRUM    ARMATURE    OF   SIX    EQUIDISTANT    TURNS,    WITH    CORRE- 
SPONDING    CURVE    OF    E.  M.  F. 


generated  in  these,  added  and  co-directed  by  the  aid  of  a  suit- 
able commutator,  will  be  represented  by  the  curve  in  the  same 
figure,  and  while  the  E.  M.  F.  generated  in  any  one  of  the 
conducting  loops  fluctuates  between  o  and  i  volt,  four  times 
per  revolution,  the  total  E.  M.  F.  produced  under  these  con- 
ditions would  vary  between  5  and  5.5  volts,  24  times  per  revolu- 
tion. In  the  same  manner,  if  instead  of  6  conducting  loops 


INDUCTION  IN  DYNAMO   ARMATURES. 


97 


being  placed  on  the  armature,  there  are  12  such  loops,  as. 
shown  in  Fig.  77,  the  total  E.  M.  F.,  if  added  and  co-directed 
by  a  suitable  commutator  as  before,  would  vary  between  10.6 
and  10.8  volts,  48  times  per  revolution,  as  shown  by  the  curve. 

109.  An  inspection  of  the  preceding  curves  of  E.  M.  F.  will 
show  that,  while  the  total  E.  M.  F.  capable  of  being  produced 
from  a  combination  of  conducting  loops,  is  less  than  the  sum 
of  the  maximum  E.  M.  Fs.  in  each  separately,  yet  their  com- 


i    - 

0 


FIG.    77. — DRUM   ARMATURE    OF    TWELVE    EQUIVALENT    TURNS,  WITH    COR- 
RESPONDING CURVE  OF  E.  M.  F. 

bined  E.  M.  F.  is  much  more  nearly  uniform  than  their  sepa- 
rate E.  M.  Fs.,  and  tends  to  become  constant  as  the  number  of 
loops  is  increased,  the  curve  of  the  total  E.  M.  F.  tending  to 
become  more  and  more  nearly  a  horizontal  straight  line. 

110.  It  must  be  carefully  remembered  that  the  E.  M.  F. 
generated  in  any  single  turn  does  not  necessarily  continue  uni- 
form during  the  passage  of  the  turn  beneath  the  pole;  or,  in 
other  words,  that  the  crests  of  the  waves  of  E.  M.  F.  are  not 
necessarily  straight  lines,  such  as  are  indicated  in  Fig.  69,  70,  71, 
and  74.  These  crests  will  be  straight  lines,  only  if,  as  hitherto 
assumed,  the  intensity  in  the  air-gap  remains  uniform  over  the 
entire  polar  surface.  In  practice  this  is  rarely  the  case.  The 
intensity  may  be  either  greater  or  less  at  the  centre  of  the  pole- 
face  than  at  the  edges,  but  is  usually  greater,  the  flux  tapering 


98 


ELECTRO-DYNAMIC  MACHINERY. 


off  toward  the  polar  edges.  This  is  owing  to  the  fact  that  the 
reluctance  in  the  magnetic  circuit  is  usually  a  minimum,  at  or 
near  the  polar  centre,  with  a  consequent  increase  in  intensity 
in  that  region.  The  same  rules  apply,  however,  even  when 
the  wave  form  of  E.  M.  F.,  as  generated  by  the  wires  singly, 
is  complex.  The  effect  of  winding  a  number  of  turns  around 


FIG.    78. — DRUM   ARMATURE    WITH    TWENTY-FOUR   TURNS   IN   BIPOLAR    FIELD. 

the  armature,  and  uniting  their  E.  M.  Fs.,  is  to  produce  an 
aggregate  E.  M.  F.  that  is  much  more  nearly  uniform  than  the 
E.  M.  F.  in  each  separate  turn. 

Thus  Fig.  78  represents  a  drum  armature  with  twenty-four 
complete  loops,  or  forty-eight  wires,  lying  over  its  surface  and 
uniformly  dispersed.  If  this  armature  be  rotated  in  a  bipolar 
field  which  is  of  such  strength  and  distribution  that  each  turn 


1.0- 


'0.5- 


«       DEGREES  ANGULAR  DISPLACEMENT 
FIG.     79. — E.    M.    F.    DIAGRAM    OF  ONE   TURN    ON    ARMATURE. 

has  induced  in  it  an  E.  M.  F.,  such  as  is  represented  in  Fig. 79, 
that  is  to  say,  no  E.  M.  F.  at  the  point  a,  about  o.  7  volt  at  £, 
a  maximum  of  about  0.95  volt  at  <:,  and  no  E.  M.  F.  at  e  ; 
then,  if  with  the  aid  of  a  suitable  commutator,  these  loops  are 
connected  together  so  as  to  unite  their  E.  M.  Fs.  into  two 
equal  series,  the  E.  M.  F.  of  the  machine  as  obtained  from  the 
brushes  on  the  commutator  is  represented  during  half  a  com- 
plete rotation  by  the  curve  in  Fig.  80,  the  corresponding 
points  of  which  are  marked  a  b  c  d  e.  It  will  be  observed  that 
there  are  twenty-four  undulations  in  this  curve,  each  undula- 


INDUCTION  IN  DYNAMO  ARMATURES. 


99 


tion  corresponding  to  the  step  between  the  entrance  of  each 
turn  under  the  pole-pieces. 

III.  Moreover,  the  shape  of  the  polar  edges  must  necessarily 
influence  the  rise  and  fall  of  the  E.  M.  F.  induced  in  each 
separate  wire  as  it  passes  beneath  the  pole.  For  example,  if 


15- 


DEGREES  AiNauLAR  DISPLACEMENT 


FIG.     80. — E.    M.  F.  DIAGRAM   OF   ARMATURE   COMBINING   E.     M.     Fs.    FROM 
SEPARATE    TURNS. 

the  area  of  the  pole-face  be  represented  by  the  shaded  area  A 
in  Fig.  81,  the  wires  passing  in  succession  beneath  this  pole, 
will  have  an  E.  M.  F.  induced  first  in  a  portion  of  their  length, 
and  finally  throughout  their  entire  length,  so  that  the  E.  M.  F. 
wave  for  each  wire  will  rise  gradually.  If,  however,  the  polar 


FIG.     8l. — DIAGRAMS    OF    POLAR    FACES    OF     DIFFERENT   OUTLINE,    OVER 

ARMATURE. 


area  be  such  as  is  represented  at  B,  the  wires  enter  the  polar 
flux  more  suddenly,  and  the  E.  M.  F.  wave  of  each  wire,  at  the 
beginning  and  end,  will  be  rendered  more  abrupt.  As  regards 
continuous-current  generators,  there  is  but  little  advantage  to 
be  gained  by  variations  in  the  shape  of  the  pole-faces,  since  the 
aggregate  E.  M.  F.  of  such  a  machine  is  rendered  nearly  uni- 


100  ELEC7^RO-DYNAMIC  MACHINERY. 

form  by  the  superposition  of  the  E.  M.  Fs.  in  the  various  wires. 
Eddy  currents  in  the  conductors  and  iron  core  are,  however, 
diminished  by  tapering  the  pole  pieces,  as  at  A. 

112.  In  studying  the  arrangement  of  the  wires  on  the  surface 
of  the  armature  in  a  generator,  with  the  view  of  determining 
the  E.  M.  F.  generated  by  the  revolution  of  the  armature,  it 
is  necessary  to  observe  that  the  E.  M.  F.  developed  does  not 
depend  directly  upon  the  length  of  the  armature  wire  which 
cuts  magnetic  flux,  but  does  depend  directly  upon  the  amount 
of  flux  enclosed  by  the  conducting  loops  during  their  revolu- 


FIG.  82. — TYPE   OF    ARMATURE    HAVING    COMPARATIVELY    LITTLE  "  IDLE  " 

WIRE. 

tion.  It  is  a  common  error  to  regard  all  the  wires  on  the  free 
surface  of  an  armature  which  do  not  pass  through  the  mag- 
netic flux  as  idle  wires  ;  and,  consequently,  detrimental  to  the 
efficient  operation  of  the  machine.  This  error  comes  from 
regarding  tfie  E.  M.  F.  as  produced  alone  by  the  cutting  of 
flux,  whereas  in  such  a  case,  as  for  example,  a  pole  armature 
(Fig.  17),  none  of  the  wire  cuts  the  magnetic  flux,  and,  conse- 
quently, would,  by  the  preceding  definition,  be  regarded  as 
idle  wire. 

In  reality,  the  generation  of  the  E.  M.  F.  is  dependent  on  the 
embracing  of  flux  by  the  loops,  and  since  the  so-called  idle  wire 
is  necessary  to  form  a  part  of  the  loop,  it  cannot  properly  be 
regarded  as  idle.  It  is,  of  course,  to  be  remarked  that  in  the 


INDUCTION  IN  DYNAMO  ARMATURES.  101 

event  of  the  conducting  loop  having  a  fairly  considerable  part 
of  its  length  formed  of  the  so-called  "idle"  wire,  in  order 
to  permit  the  loops  to  embrace  a  considerable  amount  of  flux 
during  their  revolution,  the  rate  of  cutting  flux  by  the  parts 
that  do  cut,  requires  to  be  correspondingly  increased,  thus 
requiring  a  greater  density  of  magnetic  flux. 

That  this  consideration  is  correct  may  be   seen   from   an 
inspection  of  Figs.  82  and  83. 

113.  Fig.  82  represents  a  machine  in  which  the  armature  is 
almost  completely  enclosed  by  polar  surfaces,  so  that,   even 


FIG.     83. — TYPE    OF    ARMATURE    HAVING    COMPARATIVELY    MUCH    "IDLE" 

WIRE. 

allowing  for  the  free  wire  on  the  sides  of  the  armature,  sixty 
per  cent,  of  the  length  of  the  wire  is  always  in  the  magnetic 
flux,  and  forty  per  cent,  is  "idle."  Fig.  83  shows  a  type  of 
armature  in  which  only  about  twenty-five  per  cent,  of  the 
length  of  the  wire  is  at  any  time  in  the  magnetic  flux,  so  that 
about  seventy-five  per  cent,  is  "idle."  Yet,  with  equally  ad- 
vantageous circumstances  as  regards  the  cross-section  of  the 
iron  core,  speed  of  revolution,  and  the  number  of  turns  of  wire, 
the  E.  M.  F.  from  the  machine  shown  in  Fig.  83  is  fully  equal 
to,  if  not  greater  than,  that  developed  in  the  armature  of  Fig.  82. 
If,  for  example,  the  polar  surface  in  Fig.  82  were  reduced  by 
cutting  it  away  along  the  lines  ab,  r/and  de,  thus  removing  the 
polar  edges,  and  shortening  the  polar  arc  by  about  fifty  per 


102  ELECTRO-DYNAMIC  MACHINERY. 

cent.,  the  E.  M.  F.  developed  by  the  generator  would  not  be 
reduced  if  the  same  total  quantity  of  flux  were  forced  through 
the  armature  as  before.  The  change  effected  would  be  that 
the  reluctance  of  the  air-gap,  between  poles  and  armature  on 
each  side,  would  be  increased,  since  the  cross-sectional  area  of 
the  air-gap  would  be  diminished,  and  a  greater  M.  M.  F.  would 
therefore  be  needed  on  the  field  magnets  in  order  to  produce 
the  same  flux  through  the  circuit  as  before,  but  if  this  flux 
were  reproduced,  the  amount  enclosed  with  each  turn  of  the 
armature  by  its  revolution  would  be  the  same,  and  the  total 
E.  M.  F.  induced  in  the  armature  would  be  the  same;  or, 
regarding  the  question  from  a  different  standpoint,  the  inten- 
sity of  flux  in  the  air-gap  would  be  increased  about  one  hun- 
dred per  cent.,  so  that  the  wires  would  generate  twice  as 
much  E.  M.  F.  as  before,  but  would  only  be  generating 
E.  M.  F.  about  half  the  time  in  each  revolution. 

In  other  words,  provided  the  armature  core  is  traversed  by 
a  given  magnetic  intensity,  it  is  a  matter  of  indifference  how 
much  of  its  surface  is  covered  by  pole-pieces  or  how  much 
left  exposed  with  "idle  wire,"  except  as  regards  the  amount  of 
M.  M.  F.  which  will  be  needed  to  force  the  flux  through  the 
armature. 


CHAPTER  IX. 

ELECTROMOTIVE    FORCE    INDUCED    BY    MAGNETO    GENERATORS. 

114.  One  of  the  earliest  types  of  operative  dynamos  was  that 
in  which  the  field  consisted  of  a  permanent  magnet,  and  the 
armature  was  of  the   Siemens,   or  shuttle-wound  type.     This 
armature  consists  essentially  of  a   single  coil    of  many  turns 
of  wire,  wrapped   in   a   deep   longitudinal  groove,  formed   on 
opposite  sides  of  an  iron   cylinder.     Owing  to   its  simplicity, 
this  early  type  of  magneto-electric  machine  has  survived  in  its 
competition  with  more  advanced  types,  for  such  purposes  as 
signal  calls  in  telephony,  and  for  firing  electric  fuses  in  mines. 
A  machine  of  this  type  is  shown  in  Fig.  84.     The  magnets 
J/,  J/",  are  usually  compound ;  i.  e.,  consist  of  separate  bars  of 
hardened  steel,  with  their  like  poles  associated  as  shown  in  the 
side  view.     The  magnets  are  thus  combined  to  form  a  single 
magnetic  circuit  through  the  armature,  by  means  of  soft  iron 
pole-pieces  ^'and  S'.     The  armature  core  A  A,  was  originally 
formed  of  a  single    piece   of  soft    iron,   but    is   now  usually 
laminated,  that  is,  formed  of  sheets  of  soft  iron,  laid  side  by 
side.     The  armature  winding  is  in  the  form  of  a  single  coil  or 
spool,  and  the  ends  of  the  coil  are  brought  out  to  the  insulated 
segments  of  the  two  part  commutator  C  Cf,  Figs.  85  to  88. 

115.  In  order  to  determine  the  E.  M.  F.  capable  of  being 
produced  by  a  generator  of  this  type  and  of  given  dimensions, 
it  is  necessary  first  to  ascertain  the  total  quantity  of  flux  which 
passes  through  the    armature    in  the    different    positions    it 
assumes  during  rotation.     As  shown  in  Fig.  85,  the  armature 
core  lies  at  right  angles  to  the  polar  line,  and,  consequently, 
no  flux  passes  directly  through  its  winding.     When,  during  its 
motion,  the  armature  reaches  the   position    shown  in  Fig.  86, 
where  the  end  A,  has  approached  the  north  pole,  the  flux  is 
threading  through  the  armature  in  a  direction  from  the  north 
pole  JV9  to  the  south  pole  S.     In  Fig.  87,  the  armature  core  is 

e 

or  THE 


104 


ELECTRO-D  YNAMIC  MA  CHINER  V. 


shown  as  lying  directly  between  the  pole-pieces.  In  this  posi- 
tion the  armature  gives  passage  to  the  maximum  amount  of 
flux.  In  Fig.  88,  the  armature  core  is  shown  as  moved  beyond 
this  position,  and  is  now  reducing  the  amount  of  flux  threading 
through  its  core.  Continuing  rotation  untiKthe  completion  of 
a  half  turn,  the  position  shown  in  Fig.  85,  is  reached,  but  now 


FIG.    84. — MAGNETO  GENERATOR  WITH  SHUTTLE  ARMATURE. 

in  the  reverse  direction;  /.  ^.,  with  the  end  A,  lowest  instead 
of  uppermost;  and  here  the  coil  is  emptied  of  flux  as  before. 

Il6.  It  is  evident,  from  a  consideration  of  the  preceding 
figures,  that  the  amount  of  flux  passing  through  the  armature 
in  any  position  depends  upon  the  M.  M.  F.  produced  by  the 
steel  magnets;  /.  £.,  upon  their  dimensions  and  shape,  and  on 
the  reluctance  of  the  air-gap,  that  is,  on  the  dimensions  and 
shape  of  the  pole-pieces,  as  well  as  on  the  entrefer  or  air-gap 
lying  between  the  poles  and  armature. 

For  practical  purposes,  a  steel  magnet  may  be  regarded  as 
producing  a  uniform  difference  of  magnetic  potential  between 


MAGNETO   GENERATORS.  105 

its  poles,  except  when  the  flux  passing  through  the  circuit 
represents  an  intensity  greater  than  one  kilogauss  in  the  steel. 
We  may  practically  consider  that  ordinary  hard  magnet  steel 
maintains  a  permanent  M.  M.  F.  of  10  gilberts-per-centimetre 
of  its  length,  independently  of  its  cross-section,  and  at  the 

same  time  possesses  a  reluctivity  of  -  If,  then,  the  magnets 
shown  in  Fig.  84,  are  30  cms.  long  and  have  a  total  cross- 


i- 


FIG.  87.  FIG.  88. 

FIGS.    85,  86,  87,  AND  88. — SHUTTLE- WOUND  ARMATURE   IN    BIPOLAR   FIELD. 

section  of  12  square  centimetres,  the  M.  M.  F.  they  produce 

will  be  300  gilberts,  and  their  reluctance  will  be  —  x  =  T~ 

12       150       60 

oersted.     Neglecting  leakage,  the  flux  which  will  pass  through 
the  armature  will,  therefore,  be    — webers,  where  (R,  is 


the  reluctance  of  the  two  air-gaps  in  series.     If,  then,  we  plot 


io6 


ELECTRO  D  YNAMIC  MA  CHINER  Y. 


the  total  length  of  air  space  in  cms.  (twice  the  length  of  the 
air-gap),  for  different  angular  positions  of  the  armature,  and 
divide  by  the  area  of  the  armature  beneath  one  pole  in  sq. 
cms.,  we  obtain  the  reluctance  (R,  and,  substituting  its  value  in 
the  above  equation,  we  may  determine,  approximately,  the 
magnetic  flux  through  the  armature  for  all  positions  during 
rotation. 

117.  Proceeding  in  this  manner  we  obtain  such  a  curve  as  is 
shown  in  Fig.  89,  which  represents  the  flux  passing  through 


s_10 

<_on 


on- 


_30 
>—  40 
:  —  60 


30°      60        90       120      150 

DEGREES          ANGULAR  DISPLACEMENT 
OF  ARMATURE 


—100- 

FIG.  89. — DIAGRAM  OF  FLUX  PASSING  THROUGH   ARMATURE   IN  DIFFERENT 
ANGULAR   POSITIONS. 

the  armature  core  at  different  positions  of  angular  displacement 
from  the  initial  position  shown  in  Fig.  85,  from  actual  measure- 
ments 6f  a  particular  shuttle-wound  machine  of  this  type.  An 
inspection  of  this  figure  will  show  that  at  30°  displacement  the 
flux  through  the  armature  will  amount  to  above  40  kilowebers, 
while  at  90°  displacement,  the  position  of  maximum  flux,  it 
will  reach  about  93  kilowebers.  From  this  position  the  flux 
decreases  until  its  value  is  zero  at  180°,  the  position  assumed 
by  the  armature  when  it  has  completed  one  half  of  a  rotation 
and  is  again  in  the  position  represented  in  Fig.  85,  but  in  the 
reverse  direction.  From  this  position  onward,  the  direction  of 
flux  is  reversed,  the  maximum  flux  being  reached  at  an  angular 
displacement  of  270°,  or  ^  of  an  entire  rotation,  completing  a 
cycle  at  360°. 

Il8.  Having   thus  obtained  the   value   of  the   flux  passing 
through  the  armature,  it  is  a  simple  matter  to  determine  the 


MAGNETO   GENERATORS. 


107 


E.  M.  F.  at  any  speed  of  rotation;  for,  we  have  only  to  recon- 
struct the  flux  diagram  of  Fig.  89,  to  a  horizontal  scale  of  time 
in  seconds,  instead  of  angular  displacement.  This  is  shown  in 
Fig.  90,  for  an  assumed  rate  of  rotation  of  1.5  revolutions  per 
second,  or  90  revolutions  per  minute,  the  horizontal  distance 
of  o  m,  being  taken  as  one  second,  and  the  vertical  scale 
being  taken  for  convenience  smaller  than  in  Fig.  89. 


FIG.  QO. — DIAGRAM  OF  FLUX  PASSING   THROUGH   ARMATURE   AT   DIFFERENT 
PERIODS  OF  TIME. 

The  E.  M.  F.  produced  in  any  single  loop  or  turn  around 
the  armature  will  be  the  rate  of  increase  in  the  flux  passing 
through  the  armature.  If  at  the  position  <9,  commencing  the 
curve,  we  continue  the  curve  along  the  dotted  tangent  of  O  O\ 
for  one  second  of  time,  we  reach  the  ordinate  m  Of,  of  770 
kilowebers,  and  this  is  the  rate  at  which  flux  is  entering  the 
loop  at  that  moment;  for,  if  the  rate  at  O,  were  continued 
uniformly  for  an  entire  second,  we  should  evidently  reach  the 
point  O'.  The  E.  M.  F.  existing  at  the  moment  of  starting  is, 


io8  ELECTRO-DYNAMIC  MACHINERY. 

therefore,  770,000  C.  G.  S.  units  (of  which  100,000,000  make 
one  volt)  or  0.0077  volt,  and,  if  the  number  of  turns  around 
the  armature  core  be  1,000,  the  total  E.  M.  F.  in  the  armature 
winding  will  be  7.7  volts.  Again,  if  after  a  lapse  of  %th  of  a 
second,  the  flux  curve  o  a  b  c  d  efg  hi  k  I  m  n,  be  examined, 
it  will  be  found  that  the  curve  has  reached  the  point  b,  or  its 
maximum  positive  value  when  it  commences  to  descend  toward 
g,  so  that  the  tangent  is  horizontal,  representing  that  the  rate  of 
change  of  flux  is  zero,  or  similar  to  the  condition  of  slack  water 
in  a  tide-way.  At  this  point,  therefore,  the  E.  M.  F.  in  each 
turn  on  the  armature  is  zero,  and  the  curve  of  E.  M.  F.  O  A 
BCD,  etc.,  touches  the  zero  line  at  this  point  B. 

Again  at  the  point  ^,  on  the  flux  curve,  if  the  change  of  flux 
were  to  continue  for  one  second  uniformly  at  this  rate,  we 
should  follow  the  dotted  line  or  tangent  q  q',  which  reaches 
the  ordinate  —400,  or  500  below  q ',  so  that  the  rate  of  change 
at  the  point  q,  on  the  curve  is  500  kilowebers,  represented  by 
the  point  Q,  on  the  E.  M.  F.  curve  at  that  ordinate.  Con- 
tinuing in  this  way  we  trace  the  E.  M.  F.  curve  O  A  B  C  D,  etc., 
showing  that  an  alternating  E.  M.  F.  is  produced  in  the 
armature,  varying  between  +7.7  and  — 7.7  volts.  At  the 
rate  of  rotation  assumed;  namely,  i^  revolutions  per  second, 
there  will  be  three  alternations  of  E.  M.  F.  per  second,  or 
twice  the  number  of  revolutions  in  that  time. 

119.  Having  now  examined  the  means  for  determining  the 
value  of  the  E.  M.  F.  developed  in  the  armature,  we  will  con- 
sider the  effect  of  the  commutator.  It  will  be  seen  by  refer- 
ence to  Figs.  85  to  88,  the  brushes  B,  B ',  resting  on  the 
segments  of  the  two-part  commutator,  that  the  direction  of  E. 
M.  F.  from  the  armature  toward  the  external  circuit  is  reversed 
at  the  moment  when  the  core  passes  the  position  of  maximum 
contained  flux,  as  indicated  by  the  change  in  the  direction  of 
the  dotted  loops  C  .D'  E'  and  L'  M'  N',  relatively  to  the 
horizontal  line.  The  E.  M.  F.  generated  by  the  armature  as 
produced  at  the  brushes  B,  B',  will  be  represented  by  the 
pulsating  E.  M.  F.,  O  A  B  C  D'  E  F  G  H  I K  L'  M'  N'. 
It  is  evident  that  had  we  selected  a  higher  rate  of  rotation,  the 
E.  M.  F.  of  the  machine  would  have  been  correspondingly 
increased. 


MAGNETO    GENERATORS.  109 

120.  The  preceding  considerations  can  only  determine  the 
value  of  the  E.  M.  F.  at  the  brushes,  while  the  external  circuit 
is  open.  As  soon  as  the  circuit  of  the  armature  is  closed,  the 
E.  M.  F.  at  the  brushes  is  reduced,  for  the  following  reasons; 
viz., 

(i.)  The  current  in  the  armature  always  produces  an  M.  M.  F., 
counter,  or  opposite  to  the  M.  M.  F.  of  the  field  magnet,  and, 
therefore,  diminishes  the  flux  through  the  magnetic  circuit, 
thus  causing  a  corresponding  diminution  in  the  value  of  the 
E.  M.  F.  produced.  Indeed,  this  opposing  M.  M.  F.  may, 
under  certain  circumstances,  assume  a  magnitude  sufficient  to 
neutralize  and  destroy  the  permanent  M.  M.  F.  in  the  field 
magnets.  This  is  one  of  the  reasons  why  magneto  generators 
are  not  employed  on  a  large  scale  in  practice. 

(2.)  The  current  through  the  armature  produces  in  the 
resistance  of  the  armature,  a  drop  in  the  E.  M.  F.  If,  for 
example,  the  current  through  the  armature  at  any  instant  be 
one  ampere,  and  the  resistance  of  the  armature  be  10  ohms, 
then  in  accordance  with  Ohm's  law,  the  drop  of  E.  M.  F.  pro- 
duced in  the  armature,  will  be  i  X  10  —  10  volts. 

(3.)  The  current  through  the  armature  not  being  steady,  but 
pulsating,  the  variations  in  current  strength  will  induce 
E.  M.  Fs.  in  the  coil  opposed  to  the  change  and,  therefore, 
reducing  the  effective  E.  M.  F. 


CHAPTER  X. 

POLE    ARMATURES. 

121.  The  form  of  armature,  which  stands  next  in  order  of 
complexity  to  the  shuttle-wound  armature  last  described,  is  the 
radial  or  pole  armature,  represented  in  Figs.  .91  and  92.     Here 
the  armature  coils  c,  c,  are  wrapped,  usually  by  hand,  around 
radially   extending  laminated  pole-pieces,   formed  from  sheet 
iron  punchings  laid  side  by  side.     This  type   of  machine  is 
rarely  found  in   continuous  current  generators,  but  is  some- 
times adopted  in  very  small  motors.     The  winding  of  such  an 
armature  is  carried  out  as  represented  in  Fig.  93,  where  the 
pole-pieces  are  shown  at  P  P,  and  P'  P '.     Starting  the  wind- 
ing at  the  point  M,    the  coil  A,  is  wound  from  A  to  B,  as 
shown;  the  coil  C,  is  then  wound  from  B^  through  C  to  D;  the 
coil  E,  from  Z>,  through  E  to  E;  the  coil  G,  from  F,  through 
G  to  H;  the  coil  /,  from  H9  through  J  to  K;  the  coil  Z,  from 
K,  through  L  to  My  finally  connecting  the  last  end  of  the  coil 
M,  to  the  first  end  of  the  coil  A,  thus  making  the  closed-coil 
winding  shown  in  the  figure.     The  connections  of  this  winding 
to  the  six-part  commutator  will  be  seen  from  an   inspection 
of  the  figure.     The  points  M,  B,  Z>,  E,  .//and  K,  are  branches 
connected  to  the  separate  insulating  segments  of  the  commu- 
tator, brushes  being  provided  in  the  position  shown  on  a  line 
connecting  the  centres  of  the  pole-pieces.     This  commutator 
is  shown  in  cross-section  at  P,  Fig.  92.     It  will  be  seen  that, 
owing  to  the  conical    boundaries  of   each  armature    coil,    the 
winding   is  difficult   to   arrange.     This  type    of    generator  is 
always  operated  by  an  electro-magnetic  field. 

122.  Since  the  dimensions  of  machines  with  pole  or  radial 
armatures  are  always  small,  the  reluctance   of  the   circuit  is 
practically  wholly  resident  in  the  air  spaces  between  the  poles 
and  armature  projections,  provided  care  be  taken  that  the  iron 
in  the  armature  is  not  worked  at  an  intensity  above  10  kilo- 


POLE  ARMATURES. 


Ill 


gausses,  or  above  7  kilogausses  in  the  field  magnet,  if  the  latter 
be  of  cast  iron.  If  S,  be  the  area  of  the  polar  face  of  a  radial 
armature  projection  in  square  centimetres,  and  d,  be  the  clear- 
ance or  entrefer  in  cms.,  then  —  will  be  the  reluctance  of  the 

o 

entrefer  over  each  armature  projection.     Since  there  are  four 


FIG.    91. — POLE    ARMATURE   AT   RIGHT   ANGLES   TO    AXIS. 

such  air-gaps  in  multiple-series  the  total  reluctance  of  the  cir- 
cuit   provided    in  the  case  represented,  by  Fig.    91,    will    be 


FIG.    92. — SECTION   OF   POLE   ARMATURE   THROUGH    AXIS. 

— ~r  oersteds,  assuming  that  the  reluctance  existing  in  the  iron 

o 

is  neglected. 

123.  The  distribution  of  the  flux  through  the  armature  is 
diagrammatically  represented  in  Fig.  95.  If  the  cross-section 
of  each  armature  core  be  s,  square  centimeters,  then  at  no 
time  will  there  be  less  than  two  radial  projections  carrying  the 
total  flux,  and  if  10  kilogausses  be  the  limit  permitted  by  the 


H2  ELECTRO-DYNAMIC  MACHINERY. 

reluctance  of  the  air-gap,  the  total  flux  to  be  forced  through 
the  armature  will  be  2  s  X  10,000  =  20,000  s,  webers.  The  M. 

M.  F.  necessary  on  the  field  magnets  will  be  20,000 .y  x  -~-  gil- 
berts. For  example,  if  s  =  1.3  sq.  cms.,  */  =  o.  2  cm.,  s  —  10  sq. 
cms.,  the  M.  M.  F.  required  will  be  26,000  x  0.02  =  520  gil- 
berts =  416  ampere-turns,  and  this  must  be  the  total  excitation 
included  on  the  limbs  of  the  electro-magnet. 


124.  In  order  to  determine  the  amount  of  flux  passing 
through  a  single  projection,  let  the  armature  be  considered  as 
slowly  rotated  counter-clockwise.  Starting  with  the  core  i, 


p 

FIG.  93. — DIAGRAM  SHOWING  CONNECTIONS  OF  COIL  WITH  COMMUTATOR. 

Fig.  95,  the  magnetic  flux  passing  through  it  will  be  found  by 
dividing  half  the  M.  M.  F.  by  the  reluctance  of  the  air-gap  over 

its  face,  or  —  =  13,000  webers.     As  it  moves  counter-clock- 

10 

wise  towards  2,  no  appreciable  change  is  effected  in  the  amount 
of  flux  it  carries,  until  the  advancing  edge  of  2  emerges  from 
beneath  the  polar  face  Wa.  The  flux  through  i,  rapidly  dimin- 
ishes until  before  i  becomes  halfway  between  the  pole  faces 
-A^  and  St,  it  is  entirely  deprived  of  flux.  When  the  position 
3  is  reached,  the  flux  re-enters  the  coil  of  i,  but  in  the 
opposite  direction,  and  when  it  passes  position  3,  the  total 
maximum  flux  of  13  kilowebers  is  in  the  reverse  direction.  The 
curve,  Fig.  94^  commences  at  13  kilowebers  in  the  position 
corresponding  to  i,  Fig.  91,  falls  steadily  from  B  to  (7,  and, 
after  a  short  pause,  from  C  to  Z>,  where  the  coil  lies  midway 
between  the  poles,  falls  again  from  D  to  E,  until  the  flux  is  13 
kilowebers  negative,  corresponding  to  the  position  4.  Con- 


POLE  ARMATURES. 


tinuing  at  this  value  to  F,  it  rises  to  G,  corresponding  to  the 
position  5,  and  then  pauses  at  the  zero  line,  in  the  gap  between 
"the  poles,  rising  finally  to  /,  corresponding  to  the  original 
position  i,  at  K. 

125.  The  E.  M.  F.  established  in  any  turn  of  the  coil  is  found 
by  ascertaining,  from  the  speed  of  rotation,  the  rapidity  with 
which  the  flux,  threading  through  the  coil,  changes  in  value. 
Jf,  for  example,  the  armature  be  driven  at  a  speed  of  1,500 


Q     H 


-ANGULAR 
-DISPLACEMENT 


co    5 
8 


-10 


FIG.  94. — DIAGRAM  SHOWING  FLUX  PASSING  THROUGH  ONE  ARMATURE  PRO- 
JECTION DURING  A  COMPLETE  REVOLUTION. 

revolutions  per  minute,  or  25  revolutions  per  second,  cor- 
responding to  the  time  of  0.04  second  per  revolution,  the  E. 
M.  F.  will  evidently  be  zero  at  the  positions  represented  by  the 
straight  line  A  B,  CD,  E  F,  G  H,  and  / K  of  Fig.  94,  since 
here,  the  rate  of  change  in  the  flux  is  practically  zero,  and  the 
E.  M.  F.  will  be  nearly  uniform  during  the  periods  repre- 
sented by  B  C,  D  E,  F  G,  and  H /,  since  the  rate  of  change  is 
nearly  uniform  in  one  direction  or  the  other  during  those 
periods.  As  shown  in  Fig.  97,  the  E.  M.  F.  in  the  single  turn 
on  the  projection  commencing  at  the  position  i,  is  zero  from 
o  to  b.  From  fr,  through  b'  to  ^,  the  flux  diminishing  at  the  rate 
of  13,000  webers  in  0.00433  second,  and,  therefore,  at  the  rate 
of  3,000,000  webers  (3  megawebers)  per  second,  and  since  100 
megawebers  per  second  correspond  to  an  E.  M.  F.  of  one  volt, 
the  E.  M.  F.  in  a  single  turn  is  —0.03  volt.  Assuming  10  turns 
of  wire  on  each  armature  projection,  the  total  E.  M.  F.  will 
be  —0.3  volt  at  this  period,  and  the  ordinate  bb,  represents 


,114  ELECTRO-DYNAMIC  MACHINERY. 

—0.3  volt  in  Fig.  97.  At  c'd,  corresponding  to  the  position 
C £>,  Fig.  94,  the  E.  M.  F.  is  zero,  falling  again  to  —0.3  volt 
from  d  to  e't  corresponding  to  a  change  in  flux  from  D  to  £, 
Fig.  94.  After  0.02  second  has  elapsed,  the  E.  M.  F.  re- 
verses in  direction  and  becomes  positive,  tracing  the  curve  ff1 
gg'  hti  jf  k. 

By  the  aid  of  the  commutator,  the  E.  M.  Fs.  in  the  coils, 
as  soon  as  they  change  their  direction,  are  reversed  relatively 


FIGS.  95  AND   96. — DISTRIBUTION  OF   FLUX   AND  E.  M.  F.  AT  POSITION    SHOWN. 

to  the  external  circuit,  and,  therefore,  preserve  their  direction 
externally,  as  can  be  seen  by  examination  of  Fig.  93. 

126.  We  have  thus  far  traced  the  E.  M.  F.  as  developed  in  a 
single  polar  projection,  and  so  resulting  from  the  variation  of 
flux  passing  through  it.  During  the  time  that  the  E.  M.  F.  is 
being  generated  in  this  coil,  a  similar  E.  M.  F.  is  being  gener- 
rated  in  the  other  coils,  displaced,  however,  in  time,  by  por- 
tions of  a  revolution.  As  shown  in  Fig.  96,  the  six  coils  on 
the  armature  have  E.  M.  Fs.  developed  in  them,  being  con- 
nected with  the  external  circuit  through  the  brushes  in  two 
parallel  series,  each  of  3  series-connected  coils.  Each  coil  is, 
therefore,  acting  in  its  circuit  for  one  half  of  a  revolution 
before  it  is  transferred  to  the  opposite  side,  and  while  Fig.  97 
represents  the  E.  M.  F.  generated  in  any  half  revolution  of 
one  coil,  we  have  to  consider  the  E.  M.  Fs.  coincidently 
being  generated  in  .its  next  neighbor  on  either  side.  This  is 
shown  in  Fig.  98,  where  the  E.  M.  F.  of  all  three  coils  is  de- 


POLE  ARMATURES. 


veloped  independently  on  parallel  lines  one  above  the  other, 
each  E.  M.  F.  being  a  repetition  of  that  in  Fig.  98,  but  dis- 
placed the  -J-th  of  a  complete  revolution.  Fig.  99  represents 


Ow  SECONDS 

FIG.   98. 
FIGS.    97,  98,  AND  99.— E.  M.  F.  WAVES   GENERATED  IN  POLE  ARMATURE. 

the  effects  of  combining  or  summing  these  three  separately 
generated  E.  M.  Fs.  in  the  same  circuit,  and  it  will  be  seen 
that  the  E.  M.  F.  pulsates  between  0.2  and  0.6  volt. 

i 

127.  If  the  resistance  of  the  wire  on  each  coil  be  r  ohms, 
then  the  resistance  of  the  three  coils  on  each  side  of  the  arma- 
ture will  be  3  r,  and  the  resistance  of  these  two  sides  in  parallel 
will,  except  at  changes  of  segments,  be  1.5  r,  so  that,  neglect- 
ing the  resistance  of  the  brushes  and  brush  contacts,  the  resist- 
ance of  the  armature  will  be  1.5  r  ohms. 


n6  ELECTRO-DYNAMIC  MACHINERY. 

The  current  strength  which  should  be  maintained  by   the 
generator,   when  on   short    circuit,    would,    therefore,    reach 

0.6 
amperes,  but  in  reality,  the  current  will  not  reach  this 

amount,  owing,  among  other  things,  to  the  effect  of  self-in- 
duction in  the  armature,  which,  under  load,  tends  to  check 
the  pulsations,  and,  consequently,  renders  them  more  nearly 
uniform,  thus  reducing  the  mean  E.  M.  F. 


CHAPTER   XI. 

GRAMME-RING    ARMATURES. 

128.  The  armature  of  the  dynamo-electric  machine  which 
comes  next  in  order  of  complexity,  is  that  devised  by 
Gramme,  and  now  known  generally  as  the  Gramme-ring  arma- 
ture. This  armature,  as  its  name  indicates,  belongs  to  the 
type  of  ring  armatures,  and  consists  essentially  of  a  ring-shaped 
laminated  iron  core  wound  with  coils  of  insulated  wire.  In 


FIG.    IOO. — DIAGRAM    OF   GRAMME-RING   ARMATURE   IN   BIPOLAR   FIELD, 
TWENTY-FOUR    SEPARATE   TURNS. 

the  Gramme-ring  armature  shown  in  Fig.  100,  the  core  is  a 
simple  ring  of  iron,  wound  with  24  separate  turns  of  wire, 
placed  so  as  to  be  able  to  revolve  about  its  axis  in  the  bipolar 
field  JV,  S.  Considering  the  ring  to  be  first  at  rest,  the  turns 
6,  7,  8,  18,  19  and  20  are  represented  as  being  linked  with  the 
total  flux  passing  through  the  cross-section  of  the  ring.  If  the 
total  flux  entering  the  armature  at  the  north  pole  and  leaving 
at  the  south  pole,  that  is,  passing  from  JV  to  *$*,  be  two  mega- 
webers,  then  one  megaweber  passes  through  the  upper  half  of 
the  ring,  and  one  megaweber  through  the  lower  half.  The 
loops  5,  9,  17  and  21  are  diagrammatically  represented  as  hav- 
ing 900  kilowebers  passing  through  them.  The  loops  4,  10, 
16  and  22  carry  700  kilowebers  ;  3,  u,  15  and  23  carry  500 
kilowebers  ;  2,  12,  14  and  24,  300  kilowebers  ;  while  i  and  13, 
carry  no  flux. 

117 


Il8  ELECTRO-DYNAMIC  MACHINERY. 

129.  Suppose  now,  the  ring  be  given  a  uniform  rotation  of 
one  revolution  per  second,  in  the  direction  of  the  large  arrows. 
It  is  evident,  that  at  any  instant  there  is  no  change  in  the 
amount  of  flux  linked  with  the  turns  occupying  the  positions 
6,  7,  8,  18,  19  and  20  ;  so  that,  although  these  contain  a  maxi- 
mum amount  of  flux,  they  will  have  no  E.  M.   F.   generated  in 
them.     Loops  5  and  9,  however,  are  in  a  position  at  which  the 
flux  they  contain   is  changing  ;  that   is  to  say,  the  amount  of 
flux  that  is  passing  through  them  at  each  instant   has  neither 
reached  a  maximum  nor  minimum  ;  and  the  same  is  true  with 
regard  to  the  loops  17  and  21.     In  5,  the  flux  is  increasing, 
and  in  9,  it  is  decreasing  ;  consequently,  the  E.  M.  F.  in  5   is 
directed  oppositely  to  that  in  9,  and,  according  to  rule,  is  in- 
dicated by  the  curved    arrows    (Par.    105);    for,  if   coil    5    be 
regarded  by  an  observer  facing  it  from  S,  the  flux,  as  the  ring 
moves  on,  will  thread  the  loop  in  the  opposite  direction1  to 
that  of  light  coming  from  the  face  of  the  loop,  considered  as  a 
watch  dial,  to  the  observer,  and  the  E.  M.  F.  generated  in  the 
loop  will  be  directed  counter-clockwise,  while  the  E.  M.   F.   in 
the  loop  9  must  have  the  opposite  direction.      Moreover,   simi- 
lar reasoning  will  show  that  all  the  coils  to  the  left  of  the  line 
J3  B ',  that  have  E.  M.  Fs.  generated  in  them,  will  have  these 
E.   M.  Fs.  similarly  directed  ;    /.  e.,  outwards,  as  shown,  while 
all  on  the  left-hand  side  of  the  line,  will  have  the  E.  M.  Fs. 
also  similarly  directed,  but  inwards.     Loops  i  and  13,  which 
lie   parallel  to  the  direction  of  the  flux,  will,  in  the  position 
shown,  have  no  flux  threading  through  them,  but  during  rota- 
tion, the  rate  of  change  of  flux  linked  with  them  is  a  maxi- 
mum ;    consequently,    the    E.    M.    F.    induced    in   them   is    a 
maximum. 

130.  Instead  of  conceiving  separate  conducting  loops  to  be 
wound  on  the  surface  of  the  armature,  as  shown  in  Fig.  100, 
let  us  suppose  a  continuous  coil  is  wound  on  the  surface  of  the 
armature  as  shown  in  Fig.  101,  the  first  and  last  ends  of  the 
coils  being  connected  together  so  as  to  make  the  winding  con- 
tinuous; then  it  is  evident  that  the  E.  M.  Fs.  so  acting  being 
similarly  directed  on  each  side  of  the  vertical  line  B  JB',  might 
be  made  to  produce  continuously  an  E.  M.  F.  in  the  conduct- 
ing wire.     Moreover,  if  two  wires,  or  collecting  brushes,  were 


GRAMME-RING  ARMATURES.  119 

employed  in  the  positions  B,  B ',  the  E.  M.  Fs.  from  the  two 
halves  of  the  ring  would  unite  at  the  brushes  B,  B'. 

Such  a  condition  finds  its  analogue  in  the  E.  M.  Fs.  pro- 
duced by  two  series-connected  voltaic  batteries  connected  as 
shown  in  Fig.  102,  with  their  positive  poles  united  at  B,  and 
their  negative  poles  united  at  B'.  The  figure  shows  two  bat- 
teries each  of  9  cells  connected  in  series.  Here,  as  indicated, 
all  the  cells  have  equal  E.  M.  F.  This  condition  of  affairs 
need  not,  however,  exist  in  the  Gramme-ring  analogue,  since 
the  only  requirement  is  that  the  sum  of  all  the  E.  M.  Fs. 


FIG.    101. — DIAGRAM   OF    GRAMME-RING   ARMATURE    IN    BIPOLAR   FIELD, 
TWENTY;FOUR   SEPARATE   TURNS. 

generated  in  the  coils  on1  the  right-hand  side  be  equal  to  the 
sum  of  those  on  the  left-hand  side.  In  point  of  fact,  as 
already  observed,  the  E.  M.  Fs.  are  not  the  same  in  each  of 
the  coils,  those  at  i  and  13  having  a  maximum  E.  M.  F.,  and 
those  at  7  and  19  having  zero  E.  M.  F.  Since  these  oppositely 
directed  E.  M.  Fs.  balance  each  other,  no  current  will  be  pro- 
duced in  the  armature  unless  an  external  circuit  be  provided, 
by  joining  the  brushes  B,  B'. 

131.  Figure  100  shows  no  difference  between  the  amount  of 
flux  threaded  through  the  coils  6,  7  and  8  ;  or  18,  19  and  20, 
and,  consequently,  according  to  theory,  a  total  absence  of 
induced  E.  M.  F.  in  these  coils.  In  practice,  however,  owing 
to  leakage  (Par.  77)  and  other  causes,  no  coil  is  entirely  free 
from  having  E.  M.  F.  generated  in  it. 

Moreover,  the  difference  in  the  E.  M.  F.  generated  in  coils 
13,  12,  ii  and  10,  is  not  as  great  as  might  be  inferred  from 
their  angular  position  on  the  armature,  owing  to  the  fact  that 


120  ELECTRO-DYNAMIC  MACHINERY. 

(Par.  100)  the  flux  enters  the  armature  core  nearly  uniformly 
all  around  its  surface. 

In  order  to  determine  the  total  E.  M.  F.  generated  in  such 
an  armature  as  is  represented  in  Fig.  101,  it  is  first  necessary 
to  determine  the  E.  M.  F.  generated  in  a  single  turn.  Let  us. 
consider  a  turn  starting  from  the  position  7,  and  therefore, 
generating  no  E.  M.  F.,  being  carried  by  the  uniform  rotation 
of  the  armature  in  the  direction  of  the  arrows  to  the  position 
19,  in  a  time  /  seconds.  During  this  time  the  flux  threading 

0  0 

through  it  changes  from  —  webers    in    one   direction,   to   - 

we*bers  in  the  opposite  direction,  and,  therefore,  the  change 
in  flux  linkage  will  be  $  webers,  $,  being  the  total  flux  pass- 
ing from  N  into  S,  through  the  armature.  Whatever  may  be 
the  distribution  of  flux  through  the  armature,  and  in  the  air- 
gap,  the  average  E.  M.  F.  generated  in  the  coil  during  this 

& 
time  will  be  —  C.  G.  S.  units  of  E.  M.  F.     If  the  number  of 

revolutions  made  by  the  armature  per  second  be  /z,  then  one 
revolution  takes  place  in  the  —  th  of  a  second,  and  a  half  revolu- 

tion in  the  -  th  of  a  second,  so  that  /  =  —  ,  and  the  average 

2/2  272 

E.  M.  F.  is    -  , 

—   =  2n  $ 

i 


132.  If,  for  example,  the  armature  be  revolved  at  a  speed 
of  600  revolutions  per  minute,  or  10  revolutions  per  second, 
n  —  10,  and  since  $,  has  been  assumed  to  be  2  megawebers, 
the  average  E.  M.  F.  generated  in  any  loop  in  passing  from 
the  position  7,  to  the  position  19,  will  be  20x2,000,000  = 
40,000,000  C.  G.  S.  units,  or  0.4  volt  (Par.  82).  The  same 
E.  M.  F.,  oppositely  directed,  however,  will  exist  on  the 
average  in  any  turn  on  the  right-hand  side  of  the  line  B  B  '. 
If  the  ring  were  wound  with  only  four  turns,  say  i,  7,  13  and 
19,  the  E.  M.  F.  generated  in  these  turns  when  placed  in 
series  and  connected  to  the  brushes  B  and  B',  would  evi- 
dently fluctuate  considerably;  since,  when  the  coils  occupy  the 


GRAMME-RING  ARMATURES.  121 

position  shown,  the  E.  M.  Fs.  would  be  a  maximum  in  i  and 
13,  and  zero  in  7  and  19,  while,  after  */&th  of  a  revolution,  all 
four  coils  would  be  active.  If,  however,  numerous  turns  are 
wound  on  the  coil,  it  is  evident  that  the  total  E.  M.  F. 
between  the  brushes  B  and  B ',  will  be  very  nearly  uniform, 
since  the  only  fluctuation  which  can  take  place  is  that  coin- 
cident with  the  transfer  of  a  single  turn  beneath  the  brush; 
consequently,  in  order  to  determine  the  total  E.  M.  F.  gener- 
ated by  the  rotation  of  a  Gramme-ring  armature,  it  is  only 
necessary  to  multiply  the  average  E.  M.  F.  in  each  turn  by 
half  the  number  of  turns  on  the  armature;  /.  e.,  by  the  number 


FIG.  102. — VOLTAIC  ANALOGUE  OF  E.  M.  Fs,  GENERATED  IN  GRAMME  RING. 

of  turns  active  between  B  and  B ',  on  each  side,  so  that  if  wy 
be  the  number  of  turns  on  the  armature,  counted  once  around, 

—  will  be  the  number  of  turns  active  between  brush  and  brush. 

2 

and  the  total  E.  M.  F.  on  each  side  of  the  armature  will  be 
2$nx~  =  &  n  w  C.  G.  S.  units  = volts. 

2  100,000,000 

If  w  =  24,  as  in  the  case  represented,  then  the  total  E.  M. 
F.  will  be  2,000,000  x  10  X  24  =  480,000,000  =  4.8  volts. 

133.  There  is  only  one  method,  in  practice,  of  connecting  the 
separate  coils  of  a  Gramme-ring  bipolar  armature;  namely, 
their  continuous  looping  around  the  ring  in  a  closed  coil,  as 
shown  in  Fig.  101. 

Suppose  that  it  is  desired  to  utilize  the  generated  E.  M.  Fs. 
for  the  purpose  of  supplying  a  current  to  an  external  circuit; 
it  is  then  only  necessary  to  apply  suitable  brushes,  or  con- 
ductors, at  B  and  B ',  so  as  to  rub  continually  against  the 
external  surface  of  the  turns  as  they  revolve,  making  the 
brushes  sufficiently  wide  to  maintain  continuous  contact. 


122 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


Under  these  circumstances,  during  the  rotation  of  the 
armature,  a  steady  current  will  flow  through  the  circuit  main- 
tained externally  between  Hand  B\  B,  being  the  positive  pole 
of  the  machine,  and  B ',  the  negative  pole.  Reversing  the 
direction  of  the  armature  rotation  will,  of  course,  reverse  the 
polarity  of  the  brushes,  as  will  also  the  reversal  of  the  direc- 


FIG.    103. — GRAMME-RING   SEXTIPOLAR    GENERATOR   WITH   BRUSHES   COM- 
MUTATING  ON    SURFACE  OF   ARMATURE. 

tion  of  the  magnetic  flux.  If,  therefore,  it  be  required  to 
change  the  polarity  of  the  brushes  without  changing  the 
direction  of  rotation,  it  is  only  necessary  to  reverse  the 
magnetic  flux  through  the  armature.  Fig.  103  shows  a 
Gramme-ring  sextipolar  generator,  with  the  commutating 
brushes  bearing  directly  on  the  metallic  surface  of  the  turns 
of  conductor  on  the  surface  of  the  armature.  This  method, 
however,  of  commuting  the  current  from  a  Gramme-ring 


GRAMME-RING  ARMATURES.  123 

armature  is  not  the  one  in  most  frequent  use;  for,  not  only 
are  the  conductors  upon  the  surface  of  the  armature  usually 
too  small  to  bear  brush  friction  without  destructive  wear,  but 
also  the  relative  amount  of  friction  offered  by  brushes,  placed 
upon  so  large  a  diameter,  is  considerable,  except  in  the  case 


FIG.    104.— COMMUTATION   OF     CURRENTS     FROM    A     GRAMME-RING    ARMATURE 
BY    A  COMMUTATOR. 

of  very  large  machines.  In  order  to  avoid  this,  as  well  as  for 
other  reasons,  it  is  usual  to  employ  a  special  form  of  commu- 
tator, as  represented  diagrammatically  in  Fig.  104,  where  each 
turn  is  connected  by  a  special  conductor  to  a  separately  insu- 
lated segment  of  a  commutator.  This  commutator,  therefore, 
contains  as  many  separate  segments  as  there  are  turns  on  the 


FIG.    105. — FORMS   OF   COMMUTATORS. 

armature.     Usually,  however,  there  are  many  turns  of  wire  on 
the  armature  to  each  segment  of  the  commutator. 

134.  It  is  customary,  in  practice,  to  give  a  considerable  length 
of  free  surface  to  the  commutator  bars,  so  as  to  increase  the 
surface  of  contact  and  thus  diminish  the  pressure  that  has 
to  be  applied.  Fig.  105  shows  two  forms  of  such  commutator. 
The  separate  segments  are  insulated  from  each  other  by  mica 
strips.  In  order  to  provide  for  the  connection  of  the  wires 
from  the  armature  to  the  separate  commutator  segments  or 


124 


ELEC7"RO-D  YNAMIC  MA  CHINER  Y. 


bars  B,  metal  projections  or  lugs  Z,  attached  to  the  bars,  arc 
provided.  The  bars,  after  being  assembled,  are  held  rigidly 
in  place  by  the  nut  N. 

Various  forms  of  brushes  are  provided  to  maintain  contact 


FIG.    106. — FORM   OF   GENERATOR    BRUSH. 

with  the  commutator  bars.     One  form,  consisting  of  wires  and 
strips  in  alternate  layers,  is  shown  in  Fig  106. 

135.  In  the  armature  so  far  considered,  it  has  been  supposed 
that  the  condition  as  regards  distribution  of  flux  and  the  con- 
sequent generation  of  E.  M.  F.  is  symmetrical.  It  is  possible, 
however,  that  in  the  construction  of  the  machine  this  symme- 


FIG.     IO7. DIAGRAM  REPRESENTING    INFLUENCE   OF   MAGNETIC  DISSYMMETRY. 


try  may  not  be  secured.  For  example,  in  Fig.  107,  the  pole- 
piece  S,  is  represented  as  being  considerably  further  from  the 
armature  at  its  lower  than  at  its  upper  edge,  thereby  increasing 
the  reluctance  of  the  air-gap  at  the  lower  edge,  and  producing 
magnetic  dissymmetry,  as  represented  by  the  distribution  of  flux 
arrows.  It  will  be  found,  however,  on  examination,  that 
despite  this  magnetic  dissymmetry,  the  average  E.  M.  F. 
produced  in  the  coils  would  remain  the  same,  although  the 
distribution  of  this  E.  M.  F.  among  the  different  turns  neces- 
sarily varies.  Thus  if  $,  be,  as  before,  the  total  flux  through 


GRAMME-RING  ARMATURES.  125 

the  armature,  the  lower  half  of  the  armature  may  take  a  cer- 
tain fraction  n  <P,  where  n,  is,  less  than  0.5,  while  the  upper 
half  takes  the  balance  (i  —  n)  0.  The  total  change  in  flux 
linkage  in  passing  from  the  position  7,  to  the  position  19,  will 
be  n$ — (i — ;/)  0  =  —  $,  as  before,  so  that  the  average 
E.  M.  F.  will  not  be  altered  by  the  dissymetry.  It  might  be 
supposed,  since  the  total  flux  passing  through  the  armature 
remains  the  same,  that  no  loss  exists  in  an  armature  whose  air- 
gap  is  thus  widened,  but  a  little  consideration  will  show  that 
the  increased  reluctance  in  the  magnetic  circuit  necessitates 
a  greater  M.  M.  F.  to  drive  the  same  amount  of  flux  through 


FIG.   IOS. — DIAGRAM    REPRESENTING    DISSYMMETRY    OF    WINDING. 

the  circuit,  and,  consequently,  if  the  M.  M.  F.  in  the  magnetic 
circuit  remains  the  same,  the  total  E.  M.  F.  of  the  armature 
will  be  diminished.  In  addition  to  magnetic  dissymmetry, 
-a  dissymmetry  of  armature  winding  may  exist,  such  as  shown  in 
Fig.  108,  where  the  right-hand  half  of  the  armature  is  seen  to 
be  wound  with  six  turns  while  the  opposite  half  is  wound  with 
five.  In  this  case,  supposing  the  armature  to  be  rotating, 
there  will  be,  at  the  moment  represented,  a  greater  E.  M.  F. 
in  the  right-hand  half  of  the  winding  than  in  the  left-hand  half, 
and  a  current  will  therefore  tend  to  flow  through  the  armature 
under  the  influence  of  the  resulting  E.  M.  F.,  even  when  no 
external  circuit  is  provided.  When  the  armature  has  made 
half  a  revolution  from  the  position  shown,  the  left-hand  half 
will  be  generating  a  greater  E.  M.  F.;  thus  tending  to  force 
the  current  backward.  Under  these  circumstances  there  will 
"be  produced  in  the  armature  an  oscillating  E.  M.  F.,  the 
number  of  oscillations  in  a  given  time  being  the  same  as  the 


126 


ELECTRO-D  YNA  MIC  MA  CHINER  Y. 


number  of  poles  passed  by  any  part  of  the  armature  in  that 
time.  That  is  to  say,  in  a  bipolar  machine  the  frequency  of 
the  double  oscillations  will  be  equal  to  the  number  of  revolu- 
tions of  the  armature  per  second.  In  a  quadripolar  machine  it 
would  be  equal  to  twice  the  number  of  revolutions,  and  so  on. 
These  oscillations  of  current  heat  the  armature  winding  and 
waste  energy  in  it.  Consequently,  although  symmetry  is 
everywhere  desirable  in  a  machine,  symmetry  of  armature 
winding  is  of  greater  importance  than  symmetry  of  magnetic 
flux  distribution. 

136.  The  armatures  represented  above  are  shown  diagram- 
matically  as  rings  of  circular  cross-section.     In  practice,  how- 


FIG.    ICQ. — CROSS-SECTIONS   OF   GRAMME-RING   ARMATURES. 

ever,  Gramme-ring  armatures  always  have  a  rectangular 
cross-section,  as  represented  in  Fig.  109.  We  have  seen 
that  the  E.  M.  F.  of  a  Gramme  armature,  depends  upon  the 
number  of  turns  of  wire  wound  upon  its  surface,  the  flux 
passing  through  it,  and  the  number  of  revolutions  per  second. 

The  electric  capability  of  a  machine   is  expressed  by  -  (Par. 

6)  ;  that  is  to  say,  its  capability  increases  directly  with  the 
square  of  the  E.  M.  F.  and  inversely  with  the  resistance. 
For  a  given  E.  M.  F:  of  the  armature,  it  is,  therefore,  desir- 
able to  reduce  the  resistance  as  far  as  possible,  in  order  to 
increase  the  electric  capability  of  the  machine.  The  shorter 
the  length  of  the  winding;  /.  e.,  the  shorter  each  turn,  and  the 
greater  the  cross-section  of  the  wire,  the  less  the  resistance  of 


GRAMME-RING  ARMATURES.  127 

armature.  If  R  ohms  be  the  resistance  of  all  the  wire  on  the 
armature,  as  measured  in  one  length,  then  the  resistance  of 

n 

a  bipolar  armature  will  be  --  ohms,   since  two  halves  of  the 

4 

winding  are  in  parallel;  consequently,  the  resistance  of  the 
armature  will  depend  upon  the  shape  of  its  cross-section,  since 
on  this  depends  the  length  of  each  turn  of  conductor.  A,  B, 
and  C,  Fig.  109,  represent  the  cross-sections  of  three  different 
armature  cores  having  the  same  area.  Calling  the  length  of 
one  turn  around  A,  unity,  the  length  of  a  turn  around  B,  will 
be  7  per  cent,  greater,  and  around  C,  40  per  cent,  greater. 
Consequently,  two  armatures  having  respectively  the  cross- 
sections  of  A  and  C,  and  wound  with  the  same  size  and 
number  of  turns  of  conductor,  would  have  the  same  E.  M.  F., 
if  driven  at  the  same  speed,  when  traversed,.by  the  same  flux, 
but  the  armature  C,  would  have  40  per  cent,  more  resistance 
than  the  armature  A,  and  its  electrical  capability  would  be 

about  30  per  cent,  less,  (  —  ).     It  is,  therefore,  desirable   i 

*  i  .  4 

designing  a  Gramme-ring  armature,  to  retain  a  nearly  square 
cross-section.  On  the  other  hand,  the  section  shown  at  C, 
offers  for  a  given  polar  arc,  a  larger  surface,  and,  con- 
sequently, a  lower  reluctance  to  the  passage  of  the  flux  in  the 
air-gap  or  entrefer,  than  in  the  case  of  the  section  A,  so 
that  it  may  be  sometimes  desirable  to  employ  an  armature  of 
the  type  B,  in  order  to  reduce  the  air-gap  reluctance,  and,  at 
the  same  time,  not  greatly  to  increase  the  length  of  winding. 
It  has  been  aptly  remarked  that  a  dynamo  is  a  combination 
of  compromises,  since  no  single  desideratum  in  its  design  can 
be  completely  realized. 


n 


CHAPTER  XII. 

CALCULATION    OF    THE    WINDINGS    OF    A    GRAMME-RING    DYNAMO. 

137.  In  order  to  show  the  application  of  the  foregoing 
principles  to  the  calculation  of  the  E.  M.  F.  produced  in  an 
armature  of  the  Gramme  type,  we  will  take  the  case  of  a 


FIG.    IIO. — GRAMME    TYPE    ARC    MACHINE. 

bipolar  Gramme-wound  armature  from  dimensions  given  by 
Messrs.  Owen  and  Skinner  in  a  paper  read  before  the 
American  Institute  of  Electrical  Engineers,  May  16,  1894,  to 
which  paper  the  reader  is  referred  for  fuller  particulars  of 
construction  and  results. 

Fig.  no,  reproduced  from  the  paper  referred  to,  shows  a 
vertical  and  a  longitudinal  cross-section  of  the  machine,  which 
is  a  bipolar,  constant-current,  Gramme-wound  generator,  of  the 
Wood  type,  intended  for  the  supply  of  any  number  of  arc 

128 


WINDINGS   OF  A    GRAMME-RING  DYNAMO.  129 

lamps  in  series  up  to  25,  and,  therefore,  capable  of  supplying 
a  total  E.  M.  F.  of  approximately  1,200  volts  at  terminals, 
with  a  current  strength  of  approximately,  10  amperes  and  an 
external  activity  of  about  12  KW. 

This  machine,  when  complete,  closely  resembles  the  gener- 
ator shown  in  Fig.  in.  Referring  to  Fig.  no,  the  field 
magnet  frame  of  cast  iron  is  shown  at  M,  M,  M,  M,  the  field 
coils  being  wound  on  spools  and  filling  the  spaces  indicated. 
The  shaft  of  the  machine  is  supported  in  bearings  B,  B,  and 


FIG.    III. — GRAMME  TYPE   ARC   MACHINE. 

space  is  left  on  the  shaft  for  a  commutator,  at  C,  and  a  driv- 
ing pulley  at  P".  The  bipolar  field  poles,  produced  by 
the  M.  M.  F.  of  the  magnet  coils  M,  J/,  J/,  M,  are  shown  at 
P  P,  P'  P'.  The  Gramme-wound  ring  armature  is  shown  at 
A  A  A.  The  dimensions  of  the  machine  are  indicated  in 
inches  on  the  figures. 

138.  The  field  winding  consists  of  100  Ibs.  of  No.  10  B.  &  S. 
gauge,  single  cotton-covered  copper  wire,  the  total  resistance 
of  the  four  coils  in  series  being  15.75  ohms  hot.  The  arma- 
ture core  is  composed  of  soft  charcoal  iron  wire  of  the  cross- 


13°  ELECTRO-DYNAMIC  MACHINERY. 

section  shown.  It  is  wound  in  15  layers  of  No.  10  B.  &  S. 
gauge,  and  contains  about  9,450  wires,  each  having  a  cross- 
section  of  0.00817  square  inch,  or  a  total  cross-section  of 
77.2  square  inches  =  498.1  sq.  cms.  The  armature  is 
wound  in  100  sections  of  No.  14  B.  &  S.  gauge,  double  cotton- 
covered  copper  wire,  in  57  turns  each,  or  5,700  turns,  making 
a  total  of  115  Ibs.  of  wire,  with  a  total  resistance  of  28.8  ohms 
hot,  but  which,  being  connected  in  two  parallel  halves,  as  repre- 
sented in  the  figure,  has  a  joint  resistance  between  brushes  of 
7.2  ohms.  Assuming  10  amperes  to  flow  through  the  machine, 
the  drop  in  the  armature  will  be  72  volts,  and  the  drop  in  the 
field  magnets  157.5  volts,  making  the  total  drop  in  the  machine 
229.5  volts.  When,  therefore,  the  pressure  at  the  machine 
terminals  is  1,200  volts,  the  E.  M.  F.  generated  by  the  machine 
is  practically  1,430  volts,  or  1,430  X  io8  =  1.430  X  ion  C.  G.  S. 
units  of  E.  M.  F. 

139.  The  formula  for  determining  the  E.  M.   F.  generated 
by  a  bipolar  armature  is 

E  —  ^  n  w  C.   G.  S.  units  (Par.  132). 

J7 

Consequently,  #  = • 

n  w 

The  speed  of  this  generator  is  stated  to  be  1,000  revolutions 
per  minute,  or  16.67  revolutions  per  second,  and  w,  is  5,700, 

therefore,    <£   =     /;43  X  I0 =  1.505  x  io6.      The  total 

16.67     X     5,700 

flux  through  the  armature  is,  therefore,  1.5  megawebers. 

140.  Assuming  that  the  M.  M.  F.  required  for  this  machine 
were  not  known,  it  could  be  calculated  in  the  following  way: 
We  first  determine  the  flux  density  in  the  various  parts  of  the 
circuit,   and  from  that  the  reluctivity  and  reluctance  of  the 
various  portions. 

The  cross-section  of  the  armature  core,  as  already  stated, 
is  498  sq.  cms.  and  if  the  flux  goes  through  each  side  or 
cross-section  of  the  armature,  the  intensity  in  the  armature 

is,  therefore,  -^ — 5—  =  15,060  gausses.     The  arc  covered 
498 

by  each  pole-piece  is,  approximately,  55  cms.,  and  the  effective 
breadth  6.5"  =  16.5  cms.,  so  that  the  area  of  the  polar  surface 


WINDINGS  OF  A    GRAMME-RING  DYNAMO.  131 

is,  approximately,  55  x  16.5  =  907.5  sq.  cms.  The  total  flux 
passes  through  this  surface,  and  the  mean  intensity  in  the 
r  1.5  x  io6 


air-gap  is 


9°7-5 


=  16.58  gausses. 


141.  Fig.  112  represents  diagrammatically  the  arrangement 
of  magnetic  circuits  through  the  machine,  where  M,  M,  M,  M, 
represent  the  field  magnet  cores,  P,  P'  the  pole-pieces  and  A  A 


M  M 

FIG.   112. — DIAGRAM   OF   MAGNETIC   CIRCUIT. 

the  armature.  Fig.  113,  represents  diagrammatically  the 
voltaic  analogue  of  the  magnetic  circuits,  where  Mi  M^  M3  Mt 
are  four  batteries,  whose  E.  M.  Fs.  correspond  to  the  M.  M.  Fs. 
of  the  field-magnet  coils.  J/",  and  J/3,  form  one  circuit  through 
the  field  frame,  a  certain  mean  length  of  the  pole-pieces,  and  a 
mean  length  in  the  armature  a,  together  with  the  two  resist- 
ances Rl  £z  in  the  air-gaps.  A  similar  circuit  is  provided  for 
the  E.  M.  Fs.  M^  and  J/4,  through  the  air-gap  resistances  R^ 
R^,  and  the  mean  lengths  of  armature  and  pole-pieces.  The 
equivalent  arrangement  of  circuits  is  represented  in  Fig.  114, 
where  J/",  J/",  are  E.  M.  Fs.,  each  equal  to  J/,  in  the  preceding 
figure,  while  the  resistance  of  the  double  circuit  through  the 
field  frame  is  one  half  of  that  of  either  of  the  resistances  repre- 
sented in  Fig.  113. 

142.  The  flux  through  the  field  cores  will  be  greater  than  the 
flux  through  the  armature  by  reason  of  a  certain  leakage  which 
occurs  over  the  surface  of  the  magnetic  circuit.  This  leakage 


I32 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


is  represented  diagrammatically  in  Fig.  113,  as  taking  place  in  a 
branch  circuit  or  dotted  semi-circle  around  the  field  coils,  but, 
in  reality,  the  leakage  takes  place  in  an  extended  system  of 
branched  or  derived  circuits  between  the  polar  surfaces  and 
portions  of  the  entire  field  frame.  The  calculation  of  the  vari- 
ous reluctances  in  the  air-path  offered  to  leakage  is  very  com- 
plex, and  it  is  preferable,  rather  than  to  attempt  such  calcula- 
tion, to  refer  to  experimental  data  already  acquired  with 
machines  of  similar  type.  The  leakage  factor,  or  the  ratio  of 
total  flux  through  the  field  magnet  cores  to  the  total  flux  pass- 


FIG.   113. — VOLTAIC   ANALOGUE   OF   MAGNETIC   CIRCUIT. 

ing  from  them  through  the  armature,  for  a  machine  of  this  type, 
is  approximately  1.7  ;  so  that,  since  the  useful  flux  passing 
through  the  armature  from  each  circuit  Ml  Mz  and  J/3  J/4,  Fig. 
113,  is  0.75  megaweber,  the  flux  through  the  field  cores  may  be 
taken  as  0.75  x  1.7  =  I-275  megawebers.  The  cross-section 
of  the  cores  is  found  to  be  176.8  sq.  cms.,  so  that  the  inten- 

1.275  X  io6 

sity  in  them  is,  approximately,    — J  ,  0 =  7,211  gausses. 

170.0 

143.  The  reluctivity  of  the  soft  wrought  iron  armature  at  a 
density  of  1.5  kilogausses,  is,  approximately,  0.0045  (Fig.  47), 
the  mean  length  of  the  flux  paths  through  the  armature  38  cms., 
and  the  cross  section  498  square  cms.  The  reluctance  of  each 
side  of  the  armature  #,  Figs.  113  and  114  is,  therefore, 

? °'°     ^  __  0.000343  oersted.     The  joint  reluctance  of  the 

498 


WINDINGS  OF  A    GRAMME-RING  DYNAMO.  133 

armature  will,  therefore,  be  0.00017  oersted  ;  and,  since  the 
armature  does  not  consist  of  continuous  sheets  of  iron,  but  of 
wires,  and  the  flux  has  to  penetrate  from  wire  to  wire  down- 
ward through  small  air-gaps,  the  total  effective  reluctance  of 
the  armature  will  be  approximately  o.ooi  oersted.  The  length 
of  the  air-gap  or  entrefer,  is  1.22"  =3.1  cms.,  and  the  area  as 
already  determined,  907.  5  sq.  cms.  so  that  the  reluctance  in 

each  air-gap  will  be  -^-  -  =0.003416  oersted,  the  total  reluc- 
tance in  the  air,  as  seen  in  Fig.  i  io,will  then  be  0.006832  oersted. 
The  reluctivity  of  the  cast  iron  in  the  field  frame  at  a  mean 
intensity  of  7,211  gausses,  may  be  taken  as  0.009  (Fig.  47). 
The  length  of  the  mean  path  in  the  field  on  each  side  of  the 
machine  is,  approximately,  152.4  cms.,  and  its  cross-sectional 
area  176.8  sq.  cms. ;  so  that  the  reluctance  in  each  half  of  the 

field  will  be,  approximately,  -~~   X  0.009  =  0.00776  oersted. 

170.0 

The  total  flux  being  divided  between  the  two  sides  of  the  field, 
the  joint  reluctance,  as  represented  in  Fig.  114,  will  be  0.00388 
oersted. 


The  drop  of  magnetic  poten- 
tial in  the  reluctance  of  the  Gilberts. 
armature  (0  R)  will  be,    .     .     .      1.5  x  io6  X  o.ooi  =  1,500 

The  drop  of  magnetic  poten- 
tial in  the  reluctance  of  the 
the  air, .  1.5  X  io6  X  0.006832  =  10,248 

The  drop  of  magnetic  poten- 
tial in  the  reluctance  of 

the  field, 2.55  x  io6  x  0.00388  =  9,894 

Total ;    .  •«.  • 21,642 

Since  one  gilbert  =  0.7854  ampere-turn,  the  total  M.  M.  F. 
in  the  circuit  will  have  to  be  very  nearly  17,000  ampere-turns, 
or  8,500  ampere-turns  on  each  of  the  spools  M,  M,  M,  M. 

144.  The  preceding  calculation  is  open  to  errors  from 
several  sources  in  the  absence  of  definite  experimental  data, 
namely  : 


134 


ELECTRO-D  YNA MIC  MA  CHINER  Y. 


(i.)  The  assumed  leakage  factor  may  be  inaccurate. 
(2.)  The  mean  lengths  of  the  flux  paths  in  various  portions  of 
the  circuit  may  be  inaccurate. 

(3.)  The  assumed  increase  in  the  reluctance  of  the  armature 


FIG.    114. — DIAGRAM   OF  VOLTAIC   ANALOGUE. 

due  to  its  being  formed  of  wires  instead  of  solid  sheets  may 
be  inaccurate. 

(4.)  The  reluctivity  of  the  cast  iron  employed  in  the  machine 
may  not  be  that  of  the  sample  of  cast  iron  assumed. 

In  this,  as  in  all  constant-current  machines,  means  are  pro- 
vided for  maintaining  a  nearly  constant  current  strength  in  the 
circuit,  despite  changes  in  the  load,  but  a  consideration  of  such 
means,  and  of  the  requirements  of  the  magnetic  circuit  to  per- 
mit such  regulation,  will  preferably  be  postponed  until  arma- 
ture reaction  has  been  studied. 


CHAPTER  XIII. 

MULTIPOLAR    GRAMME-RING    DYNAMOS. 

145.  A  given  type  of  bipolar  Gramme  machine  having  proved 
satisfactory  as  regards  efficiency,  ease  of  running  and  cost,  at 
a  full-load  output  of  say  10  KW,  it  may  have  to  be  determined 
whether  it  would  prove  advantageous  to   maintain  the  same 
design  for  a  machine  of  a  greater  output,  say  80  KW.     Let  us 
assume  that  the  linear  dimensions  of  the  lo-KW  machine  are 
doubled,  with  the  same  speed  of  revolution,  say  1,000  revolu- 
tions  per  minute,  maintained   in  the  larger  machine.     Then, 
assuming  the   same  magnetic   intensity  in  the  armature,   the 
electromotive  force  will  be  four  times  as  great,  since  the  area 
of  cross-section  of  the  armature,  and,  consequently,  the  total 
useful  flux,  will  be  increased  fourfold.     The  resistance  of  the 
armature  will  be  halved;  for  each  turn,  though  twice  as  long, 
will  have  a  cross-sectional  area  four  times  greater. 

The    electric  capability    of   the  smaller  machine  being  ex- 

f  (wY 

pressed  by   —   (Par.  6),  that  of  the   greater  will  be   ^-^-  = 

r  YZ  r 

g* 
32  — ,  or  32  times  greater  than  in  the  lo-KW  machine  ;  and,  if 

the  same  relative  efficiency  is  maintained  in  the  larger  machine 
the  output  will  be  32  times  greater.  The  weight  of  the  larger 
machine  would,  of  course,  be  eight  times  that  of  the  smaller, 
and  the  output  per  pound  of  weight  would,  therefore,  be  four 
times  greater  in  the  larger  machine.  In  reality,  however,  such 
a  result  is  impracticable,  as  will  now  be  shown. 

146.  Dynamo  machines  are  either  belt-driven  or  direct-driven. 
In  the  'case   of   direct-driven   generators,    the    speed    of   the 
generator  is  necessarily   limited   by  the  speed  of  the  engine, 
and  this,  for  well-known  constructive  reasons,  has  to  be  main- 
tained comparatively  low,   and  the   larger  the  generator  the 
slower  the  speed  of  rotation  that  has  to  be  practically  adopted. 

135 


136  ELECTRO-DYNAMIC  MACHINERY. 

Thus,  while  a  loo-KW  generator  is  commonly  driven  direct 
from  an  engine  at  a  speed  of  about  250  revolutions  per  minute, 
a  2oo-KW  generator  is  usually  direct 'driven  at  about  150,  and 
a  4oo-KW  generator  at  about  100  revolutions  per  minute.  In 
the  case  of  belt-driven  generators,  the  speed  of  belting  is 
usually  limited,  except  when  driving  alternators,  to  about  4,500 
feet  per  minute  ;  and,  since  larger  generators  require  larger 
pulleys,  their  speed  of  rotation  has  to  be  diminished.  While 
no  exact  rule  can  be  applied  for  determining  their  speed,  yet 
roughly,  in  American  practice,  the  speed  varies  inversely  as 
the  cube  root  of  the  output,  so  that,  when  one  generator  has 
eight  times  the  output  of  another  of  the  same  type,  the  speed 
of  the  greater  machine  would  roughly  be  half  that  of  the 
smaller. 

If  no  other  limitation  existed  besides  efficiency,  the  effect  of 
doubling  the  linear  dimensions  of  any  generator,  even  taking 
the  reduced  rotary  speed  into  account,  would  result  in  pro- 
ducing about  sixteen  times  the  output  for  eight  times  the  total 
weight;  but  large  machines  must  necessarily  possess  a  higher 
efficiency  than  small  machines,  not  only  owing  to  the  fact  that 
they  would  otherwise  become  too  hot,  the  surface  available  for 
the  dissipation  of  heat  only  increasing  as  the  square  of  the 
linear  dimensions,  while  the  weight  and  quantity  of  heat 
increase  as  the  cube  of  the  dimensions, — but  also  because  large 
machines  are  expected  to  have  a  higher  efficiency  from  a  com- 
mercial point  of  view. 

147.  Taking  into   account,    therefore,   the   reduced   rotary 
speed  of  larger  machines,  their  limits  of  temperature  elevation, 
and  their  necessity  for  an  increased  efficiency,  the  output  only 
increases,  approximately,   as  the  cube  of  their  linear  dimen- 
sions ;  and,   consequently,  the  output  of  the  larger  machine, 
per  pound  of  weight,  remains  practically  the  same  as  that  of 
the  smaller.     The  output  of  belted  continuous-current  genera- 
tors is  commonly  six  watts  per  pound  of  net  weight,  and  of 
direct-driven  multipolar  generators  about  eight  watts  per  pound 
of  net  weight.  « 

148.  We  have  already  seen   (Par.   132)  that  the   E.    M.  F. 
generated  by  a  Gramme-ring  armature,  is  $  n  w  C.  G.  S.  units, 


MULTIPOLAR   GRAMME-RING  DYNAMOS. 


137 


or  <£- — s  volts,  and  the  resistance  of  the  armature  will  be  — 
io8  4 

ohms,  if  R,  be  the  resistance  of  the  winding  measured  all  the 
way  round.  Suppose  now,  that  instead  of  employing  a  bi- 
polar machine,  we  double  the  number  of  poles  and  produce  a 
four-pole  or  quadripolar  machine,  as  shown  diagrammatically  in 
Fig.  115.  If  we  employ  the  same  total  useful  flux  $,  through 
each  pole,  the  average  rate  of  change  of  flux  through  the  turns 
on  the  armature  will  be  doubled,  since  the  flux  through  any 
turn  is  now  completely  reversed  in  one-half  of  a  revolution, 


FIG.    115. — DIAGRAM   OF   MAGNETIC    CIRCUITS    IN   QUADRIPOLAR   GRAMME 

GENERATOR. 


instead  of  in  one  complete  revolution  as  before.  The  average 
E.  M.  F.  in  each  turn  will  therefore  be  doubled.  In  Fig.  115 
the  magnetic  circuits  of  a  quadripolar  Gramme  generator  are 
shown  diagrammatically  by  the  flux  arrows.  Here,  as  will  be 
seen,  four  distinct  magnetic  circuits  exist  through  the  armature, 
instead  of  the  two  which  always  exist  in  the  armature  of  a 
bipolar  generator.  In  this  type  of  field  frame  four  magnetizing 
coils  must  be  used.  These  may  be  obtained  in  one  of  two 
ways  ;  namely, 

(i.)  By  placing  the  magnet  coils  directly  on  the  field  magnet 
cores,  as  shown  in  Fig.  116;  or, 

(2.)  By  placing  one  coil  on  each  yoke,  as  represented  in 
Fig.  117. 


'38 


ELECTRO-DYNAMIC  MACHINERY. 


149.  In  the  same  way,  if  we  employ  a  field  frame  with  six 
magnetic  poles,  as  shown  in  Fig.  118,  the  flux  will  be  reversed 
through  each  turn  of  wire  three  times  in  each  revolution,  and, 
consequently,  the  average  E.  M.  F.  in  each  turn  will  be  in- 
creased threefold  over  that  of  a  bipolar  armature.  In  Fig. 
118  there  are  six  magnetic  circuits  through  the  armature. 
Considering  any  segment  of  the  armature  underneath  a  pole 


FIG.    Il6. — QUADRIPOLAR   GENERATOR   WITH    GRAMME   ARMATURE. 

as,  for  example,  between  «2  and/,  the  turn  occupying  the  posi- 
tion at  «a,  is  filled  with  flux  in  an  upward  direction.  As  the 
armature  advances  in  the  direction  of  the  large  arrows,  the  flux 
through  this  turn  will  be  diminished,  and,  when  /it  reaches  the 
middle  of  the  pole  piece  $„  it  will  be  completely  emptied  of 
flux.  The  E.  M.  F.  in  the  loop,  during  this  portion  of  the 
revolution,  will  be  directed  outward  on  the  ring,  as  shown  by 
the  double-headed  arrows.  After  passing  the  centre  of  the 
pole  piece  S^  the  flux  through  the  loop  begins  to  increase,  but 


140 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


now  in  the  opposite  direction,  the  flux  passing  downward 
through  the  loop  instead  of  upward  as  before,  and,  as  we  have 
already  seen,  flux  entering  a  loop  in  one  direction  produces 
the  same  direction  of  E.  M.  F.  around  the  loop  as  flux  oppo- 
sitely directed  withdrawing  from  the  loop  (Par.  105).  Conse- 
quently,-the  E.  M.  F.  is  still  directed  outwards  on  the  ring,  as 
indicated  by  the  double-headed  arrows,  until  the  turn  reaches 
the  position /r  In  other  words,  the  E.  M.  F.  in  a  loop  is  simi- 


FIG.    1 1 8. — DIAGRAM   OF   SIX-POLE   GRAMME-RING   ARMATURE   AND   E.  M.    FS. 


larly  directed  during  its  motion  toward  and  from  the  same  pole; 
/.  <?.,  during  its  passage  past  a  pole.  When,  however,  the  turn 
begins  to  approach  the  pole  Niy  after  being  completely  filled 
with  the  downward  flux  at/,/  /.  e.,  as  the  flux  in  it  begins  to 
decrease,  the  direction  of  the  E.  M.  F.  in  it  reverses,  as  shown 
by  the  double-headed  arrows,  and  this  direction  of  the  induced 
E.  M.  F.  continues  until  the  turn  reaches  the  position  «r  By 
tracing  the  directions  of  the  induced  E.  M.  Fs.  in  the  various 
turns  of  the  ring,  as  shown,  it  will  be  seen  that  the  positions 
/,, /2,  and/8,  are  points  at  which  the  E.  M.  F.  is  positive,  or 
directed  outwards,  while  the  positions  nlt  n#  and  «8,  are  points 
at  which  the  E.  M.  F.  is  negative,  or  directed  inwards.  There 
will  be  no  current  passing  through  the  armature  in  the  con- 
dition represented,  if  the  winding  of  the  armature  be  sym- 
metrical, since  the  E.  M.  Fs.  in  the  various  segments  must  be 
equal  and  opposite.  If,  however,  brushes  be  applied  to  the 


MULTIPOLAR   GRAMME-RING  DYNAMOS.  141 

surface  of  the  armature  at  the  positions/,,  /3,  /,,  and  nlt  #2,  w3, 
any  pair  of  these,  including  one  positive  and  one  negative 
brush,  will  be  capable  of  supplying  a  current  through  an  ex- 
ternal circuit. 

150.  When,  therefore,  an  ordinary  Gramme-ring  winding  is 
employed,  there  will  be  one  brush  placed  between  each  pair  of 
poles,  or,  in  all,  as  many  brushes  as  there  are  poles.  Fig.  119 


FIG.    Iig. — DIAGRAM    OF   CONNECTIONS    BETWEEN   BRUSHES   OF    A   SIMPLE 
GRAMME-RING   WINDING   OF   A    SEXTIPOLAR   ARMATURE. 

represents  the  connections  employed  to  unite  the  various  seg- 
mental  E.  M.  Fs.  The  E.  M.  F.  of  the  armature  is  equal  to  that 
of  one  of  its  segments,  but  the  resistance  of  the  armature  is  in- 
versely as  the  number  of  segments  and  poles,  and  if  R,  be  the 

r> 

resistance  of  the  entire  armature  winding,  -^  will  be  the  joint 
resistance  between  brushes,  for  there  will  be  /  sections  in 

r> 

parallel,  each  of  which  will  have  —  ohms.     Consequently,  in 

P 
a   six-pole   armature,  there  will  be   six  segments  in   parallel, 

r> 

each  having  a  resistance  of  — ,  making  the  joint  resistance 
R_  R_ 

36'  °r  6* 

Fig.  1 20  represents  the  mechanical  arrangement  for  rigidly 
supporting  the  armature  of  a  direct-driven  octopolar  Gramme- 
ring  generator  with  eight  sets  of  brushes  pressing  upon  one 
side  of  the  armature,  thus  dispensing  with  the  use  of  a  separate 


142 


ELECTRO-D  Y NAM  1C  MA  CHINER  Y. 


commutator.  The  central  driving  pulley  PPP,  supports  upon 
its  arched  face  two  rings  R,R '.  These  rings  clamp  between 
them  the  armature  core,  and  are  clamped  together  by  14  stout 
bolts.  Where  the  supports  ss,  interfere  with  the  winding  of 
the  conductor  inside  the  armature,  the  conductors  are  carried 
on  the  supports  as  at  a  b  c  and  d. 


FIG.   120. — GRAMME-RING    MULTIPOLAR    ARMATURE. 

151.  It  is  not  absolutely  necessary,  however,  to  employ  six 
brushes  in  a  sextipolar  machine  ;  for,  since  in  a  machine  of  this 
type  the  three  separate  circuits  are  connected  in  parallel,  con- 
nections may  be  carried  within  the  armature  between  the 
various  segments,  permitting  of  the  use  of  a  single  pair  of 
brushes.  Thus  Fig.  121  represents  a  Gramme-ring  armature, 
wound  for  a  sextipolar  field,  with  triangular  cross-connections 
between  its  turns.  In  this  case,  the  corresponding  points  plt 
ni>  n»  nv  °f  Fig.  118,  instead  of  being  connected  to- 


MULTIPOLAR   GRAMME-RING  DYNAMOS.  143 

gather  by  brushes  externally  as  in  Figs.  119  or  120,  are  connected 
together  by  wires  internally.  It  is  not,  of  course,  necessary 
that  every  turn  on  the  armature  should  be  so  cross-connected, 
but  that  the  coils  or  group  of  turns  which  are  led  to  the  com- 
mutator should  be  cross-connected,  so  that  each  of  the  36  turns, 
shown  in  Fig.  121,  may  represent  a  coil  of  many  turns. 
Although  the  brushes  are  shown  in  Fig.  121,  as  being  placed  on 


FIG.   121. — ARMATURE   CROSS-CONNECTIONS   FOR   A    SEXTIPOLAR   GRAMME-RING 
WITH    TWO    BRUSHES. 

adjacent  segments,   yet    they    may    be  'equally    well    placed 
diametrically  opposite  to   each   other. 

Fig.  122  represents  the  corresponding  cross-connections  for 
a  quadripolar  Gramme  generator,  employing  a  single  pair  of 
brushes.  The  advantage  of  cross-connections  is  the  reduction 
in  the  number  of  brushes.  The  disadvantage  of  cross-connec- 
tions lies  in  the  extra  complication  of  the  armature  connections. 
In  large  machines  it  is  often  an  advantage  to  employ  a  number 
of  brushes  in  order  to  carry  off  the  current  effectively. 

152.  Fig.  123  is  a  representation  of  a  sextipolar  generator 
whose  magnetic  field  is  produced  by  three  magneto-motive 
forces,  developed  by  coils  placed  as  shown.  The  flux  paths 
are  represented  diagrammatically  by  the  dotted  arrows  at  A. 
Each  M.  M.  F.  not  only  supplies  magnetic  flux  through  the 
segment  of  the  armature  immediately  beneath  it,  but  also  con- 
tributes flux  to  the  adjacent  segments  in  combination  with  the 
neighboring  M.  M.  Fs. 


144 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


153.  From  the  preceding  considerations  it  is  evident  that 
while  it  is  possible  to  design  a  bipolar  generator  for  any  desired 
output,  yet,  in  practice,  simple  bipolar  generators  are  not 
employed  for  outputs  exceeding  150  KW,  and,  in  fact,  are 
seldom  employed  for  more  than  100  KW,  since  their  dimen- 
sions become  unwieldy  and  their  output,  per  pound  of  weight, 
smaller  than  is  capable  of  being  obtained  from  a  well-designed 
multipolar  machine. 

In  the  same  way,  a  quadripolar  generator  can  be  made  to 
possess  any  desired  capacity;  but,  in  the  United  States, 


FIG.    122. — CROSS-CONNECTIONS   FOR   QUADRIPOLAR   GRAMME-RING  WITH 
TWO   BRUSHES. 

practice  usually  increases  the  number  of  the  poles  with  an 
increase  in  the  output  of  the  machine.  Thus,  it  is  common  to 
employ  a  four-pole  or  six-pole  generator  for  outputs  of  from  25 
to  100  KW,  and  8  to  12  poles  for  a  generator  of  400  KW, 
capacity. 


154.  Should  the  armature  of  a  multipolar  generator  not  be 
concentric  with  \ht  polar  bore  ;  i.  e.,  if  it  is  nearer  one  particu- 
lar pole  than  any  of  the  others,  the  reduction  in  the  length  of 
the  air-gap  opposite  such  pole,  will  reduce  the  reluctance  of 
that  particular  magnetic  circuit,  and  by  reason  of  the  increased 
flux  through  the  armature  at  this  point,  induce  a  higher 
E.  M.  F.  in  the  segments  of  the  armature  adjacent  to  the  pole 


MULTIPOLAR   GRAMME-RING  DYNAMOS. 


than  in  the  remaining  segments.  If  the  armature  be  not  inter- 
connected;  i.  e.,  if  it  employs  as  many  pairs  of  brushes  as  there 
are  poles,  these  unduly  powerful  E.  M.  Fs.  can  send  no  cur- 
rent through  the  armature  as  long  as  the  brushes  remain  out  of 
contact  with  the  conductors;  for  an  inspection  of  Figs.  118 
and  119  will  show  that  no  abnormal  increase  of  E.  M.  F.  can 
exist  in  a  single  segment,  but  must  be  simultaneously  generated 
in  adjacent  segments,  and  that  such  pairs  of  E.  M.  Fs.  will 
counterbalance  each  other.  When,  however,  the  brushes  are 
brought  into  contact  with  the  armature  conductors,  thereby 
bringing  the  various  segments  into  multiple  connection  with 


FIG.    123. — SEXTIPOLAR    GRAMME-RING    SUPPLIED   BY    THREE    MAGNET    COILS. 

one  another,  a  tendency  will  exist  for  the  more  powerful 
E.  M.  F.  to  reverse  the  direction  of  current  through  the 
weaker  segments. 

155.  Whether  this  tendency  will  result  in  an  actual  reversal 
of  current  depends  upon  the  difference  of  E.  M.  F.  between 
the  segments,  their  resistance,  and  the  external  resistance  or 
load. 

Let  A  and  B,  Fig.  124,  represent  the  E.  M.  Fs.  of  any  two 
segments  in  a  multiple-connected  Gramme-ring  armature,  and 
let  the  E.  M.  F.,  E,  of  A,  be  greater  than  the  E.  M.  F.,  E', 
of  B.  Owing  to  drop  of  pressure  in  the  internal  resistance  r, 
the  pressure  e,  at  the  terminals  p,  q,  will  be  less  than  the 
E.  M.  F.,  E,  of  the  stronger  segment  A.  If  e,  is  greater 

EV 

than  E' ,  a  current  of  — ^ —  amperes  will   pass  through  the 


146  ELECTRO-DYNAMIC  MACHINERY. 

segment  B,  in  the  direction  opposite  to  that  in  which  its 
E.  M.  F.  acts.  If  <?,  be  equal  to  £',  there  will  be  no  current 
through  the  segment  B^  while  if  <?,  be  less  than  £',  a  current 
will  be  sent  through  B,  in  the  direction  in  which  its  E.  M.  F. 
acts,  but  of  strength  less  than  that  supplied  by  segment  A. 
Thus,  in  Fig.  125,  the  E.  M.  F.,  E,  of  the  stronger  segment  A, 


R 
FIG.  I24-— DIAGRAM  OF  E.  M.  FS.  IN  ADJACENT  ARMATURE  SEGMENTS. 

is  represented  by  the  ordinate  e  -j-  d.  Owing  to  the  resist- 
ance r^  in  the  segment  A,  a  drop  of  pressure  d,  will  take  place 
within  it,  and  the  pressure  at  its  terminals  will  be  e  volts. 
If  E'  be  less  than  ey  the  stronger  segment  A,  will  send  a  cur- 
rent back  through  the  segment  B,  while  if  E' ,  be  greater 
than  <?,  both  segments  will  contribute  current  through  the 
external  load  resistance  R  -ohms. 

For  example,  a  separately-excited  quadripolar  generator  of 
say  100   KW  capacity,   supplying  1,000  amperes  at  100  volts 


•r   -^ 
FIG.   125. — DIAGRAM   OF   E.    M.    Fs.    IN    ADJACENT   ARMATURE   SEGMENTS. 

terminal  pressure,  has  a  resistance  in  each  of  its  four  armature 
segments  A,  B,  C,  D,  of th  ohm;  then,  provided  its  four 

magnetic  circuits  are  balanced  or  equal,  the  full  load  on  each 
segment  will  be  250  amperes,  and  the  drop  in  each  2.5  volts; 
so  that  the  four  E.  M.  Fs.  will  be,  Fig.  126  : 

Wasted 
Power, 
Watts. 

625 
625 
625 
625 

i,oob  2,500 


E.  M.  F. 

Drop. 

Current. 

Volts. 

Volts. 

A  mperes. 

A      = 

102.5 

2-5 

250 

B       = 

102.5 

2-5 

250 

C       = 

102.5 

2-5 

250 

D      = 

102.5 

2-5 

250 

MULTIPOLAR    GRAMME-RING  DYNAMOS.  14? 

The  power  expended  in  each  segment  of  the  armature  by 

the  current  as  73^?,  will  be         ,_         =  625   watts,  and  the 


100 


total  PR  loss  in  the  armature,  2,500  watts. 

156.  Considering  one  of  the  segments,  say  C,  as  normal,  and 
that  A,  owing  to  the  magnetic  dissymmetry,  gives  an  E.  M.  F. 
two  volts  in  excess;  B,  one  volt  in  excess;  and  Dy  one  volt  in 


FIG.   126. — DIAGRAMMATIC   ARRANGEMENT   OF   E.    M.    Fs.    IN   THE   SEGMENTS 
OF    A    QUADRIPOLAR    ARMATURE. 

deficit;  the  excitation  necessary  for  1,000  amperes  total  out- 
put will  produce  (Fig.  127)  the   following  conditions;  namely, 


Wasted 

E.  M.  F. 

Drop 

Load. 

Power. 

Volts. 

Volts. 

A  mperes. 

Watts. 

A 

=            104 

4 

400 

1,  6OO 

B 

=            103 

3 

300 

900 

C 

=           102 

2 

200 

4OO 

D 

=           101 

I 

100 

100 

I,OOO 


3,000 


157.  The  effect  of  magnetic  dissymmetry  in  the  segments, 
under  the  assumed  difference  of  three  volts,  will  produce,  at 


FIG.   127. — DIAGRAMMATIC   ARRANGEMENT   OF   E.    M.    Fs.    IN   THE   SEGMENTS 
OF   A  QUADRIPOLAR   ARMATURE. 

full  load,  a  difference  of  output  among  the  segments,  ranging 
from  100  to  400  amperes,  while  the  total  power  wasted  in  the 
armature  winding  will  be  increased  20  per  cent. ;  namely, 


148 


ELEC7^RO-D  YNAMIC  MA  CHINER  Y. 


from  2,500  to  3,000  watts.  The  armature  will,  therefore,  be 
raised  to  a  higher  temperature,  owing  to  the  magnetic  dis- 
symmetry, but  this  increase  in  temperature  will  not  be 
localized,  since,  although  at  one  moment  a  greater  amount  of 
heat  is  being  produced  in  certain  segments  than  in  others,  yet, 
owing  to  the  rotation  of  the  armature,  the  portions  of  the 
armature  constituting  these  segments  are  constantly  changing. 

158.  Suppose  now  the  external  circuit  be  entirely  removed, 
the  brushes  remaining  in  contact  with  the  conductors  (Fig.  128) 


FIG.   128. — DIAGRAMMATIC    ARRANGEMENT   OF   E.   M.  FS.    IN   THE    SEGMENTS 
OF    A   QUADRIPOLAR    ARMATURE. 

so  that  the  circuits  through  the  armature  segments  are  com- 
plete ;  then  the  following  conditions  will  hold  : 

Wasted 
Power. 
Watts. 

225 
25 
25 

225 


E.  M.  F. 

Drop. 

Current. 

Volts. 

Volts. 

A  mperes. 

A 

-           104 

i.S 

150 

B 

=            103 

0.5 

50 

C 

=            102 

-0.5 

-50 

D 

=            IOI 

-1-5 

-150 

o  500 

An  inspection  of  these  values  shows  that  a  difference  of 
three  volts  between  the  E.  M.  Fs.  of  the  four  segments,  pro- 
duces a  reversal  of  current  through  C  and  Z>,  at  no  load,  with 
a  useless  expenditure  of  500  watts.  Consequently,  between  no 
load  and  full  load,  there  will  be  a  change  from  an  expenditure 
of  power  with  reversal  of  current  in  the  weaker  segments,  to 
an  excessive  drop  and  expenditure  of  power  without  reversal  of 
current. 

159.  Although  this  difficulty,  arising  from  the  unbalanced 
magnetic  position  of  the  armature,  does  not,  in  practice,  give 


MULTIPOLAR   GRAMME-RING  DYNAMOS.  149 

rise  to  any  serious  inconvenience,  when  mechanical  construc- 
tion is  carefully  attended  to,  yet  windings  have  been  devised 
by  which  it  maybe  altogether  avoided.  For  example,  if  all  the 
turns  be  so  connected  that  their  E.  M.  Fs.  are  placed  in  series, 
then  a  single  pair  of  brushes  will  be  capable  of  carrying  the 
current  from  the  entire  armature,  which  will  only  be  divided 
into  two  circuits;  or,  the  segments  may  be  so  interconnected 
that  turns  in  distant  segments  may  be  connected  in  series  so  as 
to  obtain  a  more  general  average  in  the  total  E.  M.  F.  Such 
windings  are  always  more  or  less  complex,  and  the  reader  is 
referred  to  special  treatises  on  this  subject  for  fuller  details. 


160.  The  formula  for  determining  the  E.  M.  F.  of  a  multi- 
polar  Gramme  generator  armature  is, 

E  —  3>nw  C.  G.  S.  units,  where  $,  is  the  useful  flux  in 
webers,  or  the  flux  entering  the  armature  through  each  pole,  «, 
the  number  of  revolutions  per  second  of  the  armature,  and  «/, 
the  number  of  turns  on  the  surface  of  the  armature  counted 
once  around.  If,  however,  the  armature  be  series  connected, 
so  that  instead  of  having  /,  circuits  through  it  between  the 
brushes,  where/,  is  the  number  of  poles,  there  are  only  two 

circuits,  then  the  E.  M.  F.  will  be  E  =  —  3>nw,  while  if,  as  in 

some  alternators,  the  circuit  between  the  brushes  be  a  single 
one,  the  mean  E.  M.  F.  of  the  armature  will 


161.  Fig.  129  represents  the  magnetic  circuits  of  an  octopolar 
generator,  the  dimensions  being  marked  in  inches  and  in  centi- 
metres. The  field  frame  is  of  cast  steel,  and  the  armature 
core  is  formed  of  soft  iron  discs.  Let  us  assume  that  there 
are  768  turns  of  conductor  in  the  armature  winding,  and  that 
the  speed  of  rotation  is  172  revolutions  per  minute,  or  2.867 
per  second. 

Assuming  an  intensity  of  9,500  gausses  in  the  armature,  it 
may  be  required  to  determine  the  E.  M.  F.  of  the  machine. 

The  cross-section  of  the  armature  is  31.1X13  =  404.3  sq. 
cms.,  but  allowing  a  reduction  factor  of  0.92  for  the  insulating 
material  between  the  discs,  the  cross-section  of  iron  is  372 
sq.  cms.  The  total  flux  passing  through  the  cross-section  of 


150  ELECTRO-DYNAMIC  MACHINERY. 

the  armature  will,  therefore,  be  372  x  9,500  =  3,534,000 
webers. 

The  useful  flux  through  each  pole  will  be  twice  this  amount, 
or  7,068,000  webers,  so  that  the  E.  M.  F.  of  the  generator 
will  be  : 

E—  $nw  =  7,068,000  X  2.867  X  768  =  r-557  X  io10  = 
155.7  volts. 

This  will  be  the  E.  M.  F.  of  the  generator,  provided  all  the 


FIG.  129. — GRAMME-RING  OCTO POLAR  GENERATOR. 


armature  segments  are  connected  in  parallel,  as  shown  in  Fig. 
115.  If,  however,  the  armature  winding  be  so  connected  that 
only  a  single  pair  of  brushes  and  a  single  pair  of  circuits  exist 
through  the  armature,  the  E.  M.  F.  would  be  4  times  as  great, 
while  if  the  armature  could  be  connected  in  a  single  series,  the 
E.  M.  F.  would  be  8  times  as  great. 

162.  In  order  to  determine  the   M.  M.  F.  necessary  to  drive 
this  flux  through  the  armature  we  proceed  as  follows:  viz., 


MULTIPOLAR    GRAMME-RING  DYNAMOS. 


Cross-section. 
Sg.  cms. 

Flux. 
Webers. 

Intensity. 
Gausses. 

Length 
Cms. 

•6n  i$^ 

9,188,400 

13,430 

40 

354  S 

3,534,000 

9,980 

76 

*64J7V 

3,534,000 

9,500 

50 

We  first  determine  the  cross-section,  the  mean  length,  and 
the  intensity  in  each  portion  of  the  magnetic  circuits.  One  of 
the  eight  magnetic  circuits  through  the  armature  is  represented 
by  the  dotted  arrows  at  A  (Fig.  129).  We  may  assume  that  the 
flux  through  the  cores  is  7,068,000  x  1.3  =  9,188,400  webers; 
1.3,  being  the  approximate  leakage  factor  for  a  machine  of 
this  type;  in  other  words,  of  all  the  flux  passing  through  the 

cores  —  X  100    =    76.9    per    cent.,    approximately,    may    be 

O 

assumed  to  pass  through  the  armature,  half  through  each  cross- 
section.     Consequently,  we  have  the  following  distribution  : 


Field  core, 
Yoke,      . 
Armature, 


The  entrefer,  or  gap,  of  copper,  air  and  insulation,  existing 
between  the  iron  in  the  armature  and  in  the  pole  faces,  is  1.5 
centimetres  in  length,  while  the  polar  area  is  41  cms. 
X  34  cms.,  or  1,400  sq.  cms.  in  cross-section.  From  these 
data,  the  reluctance  in  the  magnetic  circuit  through  the 
armature  is 


Field  core, 

n         t  c 

Yoke, 
Entrefer,  . 

Armature, 


The  M.  M.  F.  required   to    drive  a    total    flux  of  3,534,000 
webers  through  this  circuit  will  be 


Cross-section 
carrying 

Cross- 

armature 

Length. 
Cms. 

Intensity. 
Gausses. 

Reluctivity. 

section. 
Sq.  cms. 

flux. 
Sq.  cms. 

Reluctance. 
Oersted. 

40 

13,430 

O.OO2 

342^ 

263.1 

0.000,304 

40 

13,430 

0.002 

342  • 

263.1 

O.OOO,3O4 

76 

9,980 

O.OOI 

354* 

354-0 

0.000,215 

1-5 

I. 

700  i/ 

0.002,142 

1-5 

I. 

700  v' 

O.OO2,I42 

50 

9,500 

0.0008 

372^ 

372 

0.000,107,5 

0.005,214,5 

3,534,000  x  0.005,214 


(18, 
t,5=1  i4, 

(7,3 


,430  gilberts. 
T,66s  ampere-turns. 
333  ampere-turns  on  each  spool. 


With  600  turns  on  each  spool,  the  current  would  be  12.22 
amperes. 


CHAPTER  XIV. 

DRUM    ARMATURES. 

163.  The  drum  armature  was  first  introduced  into  electrical 
engineering  by  Siemens,  in  the  shape  of  the  shuttle  armature, 
and  was  modified  by  Hefner-Alteneck  in  1873.  The  drum 
armature  was  subsequently  modified  in  this  country  by  the 
introduction  of  a  laminated  iron  armature  core,  consisting  of 
discs  of  soft  iron,  called  core  discs,  provided  with  radial  teeth 
or  projections.  This  armature  core,  when  assembled,  had 


FIG.    130.— TOOTHED-CORE  ARMATURE  IN  VARIOUS  STAGES    OF    CONSTRUCTION, 

space  provided  between  the  teeth  for  the  reception  of  the 
armature  loops  on  its  surface,  a  completed  armature  showing, 
when  wound,  alternate  spaces  of  iron  and  insulated  wire,  and 
formed  what  is  called  a  toothed-core  armature.  Next  followed 
the  smooth-core  drum  armature,  that  is,  a  drum  armature  com- 
posed of  similar  core  discs  in  which  the  teeth  were  absent,  so 
that  the  completed  armature  had  its  external  surface  com- 
pletely covered  with  loops  of  insulated  wire.  Fig.  130  shows 
a  common  type  of  toothed-core  armature  in  various  stages 
of  construction.  The  laminated  iron  core  is  shown  at  A,  as 
assembled  on  the  armature-shaft  ready  to  receive  its  winding 
of  conducting  loops  in  the  spaces  between  the  radially  project- 
ing teeth.  At  B,  is  shown  the  same  core  provided  with  wind- 

152 


DRUM  ARMATURES. 


153 


ings  of  insulated  wire.  At  C,  is  shown  a  completed  armature. 
The  detailed  construction  of  a  laminated  armature  core  is 
illustrated  in  Fig.  131,  which  shows  a  portion  of  a  drum  arma- 
ture core  already  assembled  by  the  aid  of  large  bolts  passing 


FIG.    131. — TOOTHED-CORE   ARMATURE    IN   PROCESS   OF   ASSEMBLING. 

through    holes    in    the    core-discs.     On    the   right   are   other 
core-discs  ready  to  be  placed  in  position  on  the  shaft. 

164.    Fig.    132  shows  a   laminated    armature    body  of    the 
smooth-core  type.     Here  the  separate  core-discs  are  formed 


FIG.    132. — SMOOTH-CORE   ARMATURE   BODY. 

of  sheet  iron  rings  assembled  on  the  armature,  shaft  as  shown. 
These  discs,  after  being  assembled,  are  pressed  together 
hydraulically.  The  end  rings  are  heavy  bronze  spiders,  held 


154  ELECTRO-DYNAMIC  MACHINERY. 

together  internally  by  six  bolts  shown  in  the  figure.  When  the 
armature  body  is  subjected  to  compression,  these  bolts  are 
tightened  on  the  spiders,  which  are  firmly  keyed  to  the 
shaft,  so  that  on  release  of  the  hydraulic  pressure,  the  lami- 


FIG.    133. — COMPLETED    ARMATURE,    SMOOTH-CORE   TYPE." 

nated  iron  core  forms  one  piece  mechanically.     Fig.  133  shows 
the  same  armature  completely  wound. 

165.  In  the  drum  armature,  the  conducting  wire  is  entirely 
confined  to  the  outer  surface,  and  does  not  pass  through  the 


FIG.    134. — TYPICAL   FORM   OF   SMALL   SIZE   DRUM    ARMATURE. 

interior  of  the  core.  In  this  respect,  therefore,  it  differs  from 
the  Gramme-ring  armature,  already  described,  in  which  the 
winding  is  carried  through  the  interior  of  the  core,  lying, 
therefore,  partly  on  the  interior  and  partly  on  the  exterior. 
The  armature  core,  or  body,  of  a  Gramme-ring  machine  differs 
markedly  in  appearance  from  the  armature  body  of  a  drum 
machine,  when  both  are  in  small  sizes,  since  then  the  drum  core 
is  practically  solid,  having  no  hollow  space,  so  that  it  would 
be  impossible  to  wind  it  after  the  Gramme  method.  Such  a 
drum-wound  armature  is  shown  in  Fig.  134.  When,  however, 


DRUM  ARMATURES.  155 

the  drum  armature  is  increased  in  size,  so  as  to  be  employed 
in  multipolar  fields,  the  form  of  the  core  or  body  passes  from 
a  solid  cylinder  to  that  of  an  open  cylinder  or  ring,  as  is 
shown  in  Figs.  132  and  135,  so  that  it  would  be  possible  to 
place  a  conducting  wire  on  such  a  core  either  after  the  drum 
or  Gramme  type  of  winding.  The  tendency,  however,  in 
modern  electrical  engineering  is,  perhaps,  toward  the  produc- 
tion of  drum-wound  rather  than  Gramme-wound  generators. 


FIG.    135. — LARGE    DRUM    ARMATURE   FOR    MULTIPOLAR    FIELD. 

This  tendency  has  arisen,  probably  more  from  mechanical 
and  commercial  reasons  than  from  any  inherent  electrical 
objections. to  armatures  of  the  Gramme-ring  type. 

166.  The  windings  of  drum  armatures  are  numerous  and 
complicated  in  detail,  but  all  may  be  embraced  under  two  typi- 
cal classes  ;  namely,  lap-winding  and  wave-winding.  In  lap- 
winding,  the  wire  is  arranged  upon  the  surface  of  the  armature 
in  conducting  loops,  the  successive  loops  overlapping  each 
other,  hence  the  term;  while  in  wave-winding,  the  conducting 


156  ELECTRO-DYNAMIC  MACHINERY. 

wire  makes  successive  passages  across  the  surface  of  the 
armature,  while  being  advanced  around  its  periphery  in  the 
same  direction. 

167.  Lap-winding  is  applicable  particularly  to  bipolar  arma- 
tures,  while    wave-winding    is   applicable    only   to    multipolar 

armatures. 

b 


ti 

FIG.    136. — SIMPLE   BIPOLAR   DRUM-WINDING. 

The  simplest  form  of  lap-winding  is  shown  in  Fig.  136,  where 
the  separate  paths  taken  by  the  turns  ay  b,  c,  d,  and  <?,  f,  g,  /i, 
across  the  outside  of  the  bipolar  armature  core,  and  their  con- 
nections to  the  commutator,  are  represented  as  shown.  If  the 


FIG.    137. — SIMPLE   BIPOLAR   DRUM-WINDING   WITH    LEAD    IN    COMMUTATOR 
CONNECTIONS. 

entire  winding  of  the  armature  be  completed,  it  is  evident 
that  any  attempt  to  represent  the  winding  graphically  by  the 
method  adopted  in  this  figure  would  lead  to  great  complexity. 
For  this  reason  it  is  customary  to  represent  the  armature  sur- 
face as  unrolled,  or  developed  upon  the  plane  of  the  paper,  as 


DR  UM  ARM  A  TURKS. 


'57 


shown  in  Fig.  138.  For  example,  the  winding  already  shown 
in  Fig.  136  becomes  on  this  development  represented  as  in 
Fig.  138.  Here  it  is"  clear  that  each  loop  overlaps  its  prede- 


r 


FIG.    138. — DEVELOPMENT   OF   LAP-WINDING    IN    FIGS.    136   AND    137- 

cessor,  and,  consequently,  it  is  evident  that  the  simplest  form 
of  drum-winding  is  a  lap-winding. 

Fig.    137  represents  the  same  winding  as  Fig.    136,  except 


P        g 

FIG.    139. — QUADRIPOLAR  WAVE-WINDING. 

that  the  connections  with  the  commutator  are  given  a  lead  of 
90  degrees,  requiring  a  correspondingly  altered  position  of  the 
brushes  of  the  machine. 

Fig.  139  represents   a  number  of  conductors,  ab,  cd,  ef,  gh, 


i58 


ELECTRO-DYNAMIC  MACHINERY. 


etc.,  wound  on  the  external  surface  of  a  drum  core  in  the 
winding  of  the  wave  type.  Here  it  will  be  seen  that  the 
conducting  wire,  after  crossing  over  from  one  side  of  the 
armature  core  to  the  other,  advances  progressively  over 
its  surface  in  the  form  of  a  rectangular  wave.  The  corre- 
sponding development  is  shown  in  Fig.  140.  The  winding 
shown  is  applicable  only  to  multipolar  fields  ;  for,  an  inspec- 


FIG.    140. — DEVELOPMENT   OF   QUADRIPOLAR   WAVE-WINDING. 

tion  of  this  particular  arrangement  of  wave-winding  will  show 
that  when  conducting  wires  ab  and  ef  are  passing  north  poles, 
the  conducting  wires  cd  and  gh,  are  passing  south  poles,  and 
the  direction  of  the  induced  E.  M.  F.  while  opposite  in  succes- 
sive conductors,  as  regards  the  separate  conductors  ab,  cd,  ef, 
and  ghy  is,  nevertheless,  unidirectional,  so  far  as  the  entire  cir- 
cuit a,  b,  c,  d,  e,  /,  g,  h,  i,  /,  k,  is  concerned.  In  the  same 
manner  a  wave-winding  for  an  octopolar  machine  is  required 
to  be  spaced  in  accordance  with  the  successive  distances 
between  alternate  poles. 


CHAPTER  XV. 

ARMATURE    JOURNAL    BEARINGS. 

168.  Even  in  the  best  designed  types  of  electro-dynamic 
machinery,  there  are  certain  losses  of  electric  energy  which 
necessarily  occur  in  the  operation  of  the  machine.  These 
losses  may  be  grouped  under  the  general  head  of  frictions, 
and  include  mechanical,  electric,  and  magnetic  frictions. 
Since  in  well-designed  types  of  large  machines  the  commercial 
efficiency  may  be  as  high  as  95  per  cent,  it  is  evident  that  the 


T 


FIG.    141. — SIGHT-FEED    LUBRICATED    BEARING. 


losses  from  all  these  causes  combined  can  be  kept  within  a 
small  percentage  of  the  total  output. 


169.  This  high  efficiency,  however,  can  only  be  obtained  in 
the  case  of  large  machines.  In  those  of  smaller  output,  the 
proportion  of  the  losses  may  be  much  greater.  It  is,  there- 
fore, advisable  to  examine  the  causes  of  these  various  losses, 
their  variation  with  the  output  of  a  machine,  and  the  means  by. 
which  they  are  commercially  reduced. 


159 


160  ELECTRO-DYNAMIC  MACHINERY. 

Considering  first  the  mechanical  losses  :  these  may  exist 
as  friction  in  the  bearings  of  the  moving  parts  of  the  generator, 
friction  arising  from  the -pressure  of  the  brushes  on  the  com- 
mutator, or  contact  parts,  and  friction  from  air  churning. 

The  journal  bearings  are  lubricated  either  by  sight-feed 
oiling,  or  self-oiling  devices.  In  sight-feed  oiling  devices,  a  glass 
oil  cup,  filled  from  time  to  time  with  oil,  allows  oil  to  drop  slowly 
on  the  journal  bearings,  but  requires  to  have  its  outlets  opened 
by  hand,  when  the  machine  commences  to  run,  and  also  to  be 
stopped  when  the  machine  stops. 

Fig.   141  represents  an  end  view  and  longitudinal  section  of 


FIG.    142. — DETAIL   OF   SELF-OILING   BEARING. 

such  a  bearing.  The  oil  cup  C  C,  is  provided  with  a  head  H, 
by  the  rotation  of  which  an  outlet  in  the  base  is  adjusted. 
The  oil  descends  by  gravity  to  the  shaft  6"  Sy  where,  by  the 
movement  of  the  shaft,  it  is  mechanically  carried  through 
spiral  grooves  on  the  inner  surface  of  the  babbitt-metal  sleeve 
B  B,  passing  finally,  from  the  ends  on  the  bearing,  into  the 
pans  PPt  whence  it  is  drawn  off  at  intervals  and  filtered. 

The  upper  pan,  P,  is  intended  to  catch  any  overflow  of  oil 
that  may  occur  during  the  process  of  filling.  The  box  X  X, 
enclosing  the  babbitt-metal  sleeve,  is  capable  of  rotation  within 
small  limits,  about  a  vertical  axis,  upon  the  spherical  surfaces 
ZZ.  This  play  admits  of  the  true  alignment  of  the  bearings  to 
the  shaft  S  S.  As  soon  as  the  shaft  has  been  introduced  and 


ARMATURE  JOURNAL   BEARINGS. 


161 


becomes  self-aligned,  any  further  undue  play  in  the  bearing  is 
prevented  by  tightening  the  nuts  N  N. 

170.  Sight-feed  lubricating  bearings  necessitate,  as  already 
observed,  the  opening  and  closing  of  the  oil  cup  at  the  start- 
ing and  stopping  of  the  machine.  They  have  been,  conse- 
quently, almost  entirely  replaced  by  self-oiling  bearings,  which 
require  no  such  attention;  here  the  oil  is  automatically  fed  to 
the  revolving  shaft  by  its  rotation.  A  self-oiling  bearing  of 
this  description  is  represented  in  Fig.  142.  The  oil  is  supplied 
to  the  bearing  into  the  oil  well  O  O,  through  a  screw  hole  h. 


FIG.    143. — LONGITUDINAL   SECTION   OF   SELF-OILING   BEARING. 


During  the  rotation  of  the  shaft  S  S,  two  rings  r,  r,  which  rest 
upon  the  upper  surface  of  the  shaft,  and  dip  into  the  oil  within 
the  well,  are  set  in  rotation,  and  carry  oil  on  the  surface  of  the 
shaft,  where  it  is  spread  over  the  bearing  along  suitable 
grooves  in  the  babbitt-metal  sleeve,  as  in  the  previous  case. 
Grooves  are  made  in  the  upper  surface  of  the  babbitt-metal 
sleeve  for  the  reception  of  the  rings,  and  the  rings  are  pre- 
vented from  leaving  the  grooves  by  the  screw  clips  m,  m.  The 
rings  are  carried  around  by  the  friction  caused  by  their  weight 
as  they  rest  on  the  shaft,  and,  therefore,  do  not  necessarily 
rotate  as  rapidly  as  the  surface  of  the  shaft.  The  babbitt- 
metal  sleeve,  which  holds  the  shaft,  is  contained  in  a  cylindri- 
cal box  with  a  spherical  bolt  B,  at  its  centre.  A  pin  or  pro- 


162 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


jection/,  at  the  bottom  of  this  box,  engages  in  a  hole  in  the 
frame  work,  thus  preventing  the  box  from  rotating  with  the 
shaft,  but  enabling  the  shaft  to  align  itself  freely  in  the  sleeves. 
Nuts  n,  of  which  only  one  is  seen,  clamp  the  box  B,  in  position. 


FIG.    144. — SLEEVE    OF    BABBITT    METAL    IN   JOURNAL   BEARING. 

A  draw-off  cock  is  provided  at  d,  for  withdrawing  the  oil   from 
the  well  at  suitable  intervals. 

171.  Fig.   143  represents   a   longitudinal  cross-section  of  a 
similar  bearing  employed  in   machines  of  larger  size.     Here 


FIG.    145. — DETAILS   OF    LARGE    SELF-OILING   JOURNAL   BEARING. 

oil  is  fed  through  two  openings/,  /,  and  accumulates  in  the 
lower  part  of  the  hollow  cast-iron  support  S  S.  The  rings  r,  r, 
by  their  revolution  upon  the  shaft,  carry  the  oil  into  the 
babbitt-metal  sleeve  bbbb,  as  before.  The  shaft  is  supported 
upon  the  bracket//,  which  forms  part  of  the  pedestal  or  sup- 
port 6"  S,  and  is  hollowed  spherically  so  as  to  permit  of  the 


ARMATURE  JOURNAL   BEARINGS.  163 

alignment  of  the  babbitt-metal  sleeve  and  its  box.  Fig.  144 
shows  a  general  view  of  the  babbitt-metal  sleeve  with  grooves 
for  the  reception  of  the  oil  rings,  and  with  lugs  Z,  Z,  Z,  for 
assisting  in  the  aligning.  Fig.  145  represents  partly  in  eleva- 
tion, and  partly  in  longitudinal  section,  a  similar  bearing  some- 
times employed  in  still  larger  machines,  differing  from  the  last 
described  only  in  details  of  construction.  The  weight  of  the 
shaft  is  taken  directly  upon  the  lower  half  of  the  bearing 
B  B  B,  which  has  its  lower  surface  bowl-shaped,  and  fitting 
into  a  pedestal  or  support  SS,  in  such  a  manner  that  the  bear- 
ing can  be  readily  aligned  and  finally  tightly  secured  in  place 
by  suitable  bolts.  The  gauge  glass  7",  enables  the  level  of  the 
oil  in  the  bearing  to  be  clearly  discerned. 

172.  The  amount  of  energy  expended  as  friction  in  journal 
bearings  varies  with  the  weight  supported  on  the  bearing,  the 
accuracy  of  the  workmanship,  the  correctness  of  the  alignment, 
the  nature  of  the  lubricating  material,  the  character  of  the 
surfaces  in  contact,  the  speed  of  rotation  and  the  diameter  of 
the  shaft. 

Other  things  being  equal,  the  energy  expended  is  propor- 
tional to  the  diameter  of  the  journal  in  the  bearing.  In  order 
to  keep  the  friction  as  low  as  possible,  the  diameter  of  the 
journal  is  always  kept  as  low  as  is  consistent  with  ample 
mechanical  strength. 

The  power  expended  in  brush  friction  depends  upon  the 
number  of  brushes  and  the  pressure  with  which  they  bear  upon 
the  commutator.  It  also  increases  with  the  diameter  of  the 
commutator  and  with  the  speed  of  rotation  of  the  armature. 
This  waste  of  energy  is  often  an  appreciable  fraction  of  the 
total  waste  in  a  small  machine,  but  is  usually  quite  negligible 
in  a  large  one. 


CHAPTER  XVI. 

EDDY    CURRENTS. 

173.  During  the    rotation    of  the  armature  of  a  dynamo- 
electric  machine  through  the  flux  produced  by  its  field  magnets, 
electromotive  forces  are  not  only  generated  in  the  conducting 
loops  on  the  armature,  by  the  successive  filling  and  emptying 
of  these  loops  with  flux,  but  they  are  also  generated  in  all 
masses  of  metal  revolving  through  the  flux;  in  other  words, 
the  iron  in  the  armature  core  and  the  copper  of  the  conductors 
will  also  be  the  seat  of  E.  M.  Fs.     Though  these   E.  M.  Fs. 
may  be  locally  very  small,  yet,  since  the  resistances  of  their 
circuits  are  generally  exceedingly  small,  the  strength  of  the 
currents  set  up  may  be  very  considerable. 

Such  currents  are  generally  known  as  eddy  currents.  They 
are  necessarily  alternating  in  character,  their  frequency  de- 
pending upon  the  speed  of  revolution  and  upon  the  number 
of  poles. 

Not  only  is  the  energy  expended  in  eddy  currents  lost  to  the 
external  circuit,  since  these  currents  cannot  be  made  to  con- 
tribute to  the  output,  but  such  currents  also  unduly  limit  the 
output  of  the  armature,  by  raising  its  temperature,  independ- 
ently of  the  increase  of  temperature  due  to  the  passage  of  the 
useful  armature  current  through  the  conducting  loops.  Losses 
of  energy  due  to  eddy  current  are  of  the  type  /a  R  (in  watts), 
/,  being  the  strength  of  the  local  current  in  amperes,  and  R> 
the  resistance  of  the  local  circuit  in  ohms. 

174.  It  is  evident  that    a  dynamo  machine  can   never  be 
designed  so  as  to  be  entirely  free  from  eddy  currents;  for,  con- 
ducting loops  must  be  placed  on  the  armature,  and,  moreover, 
in  nearly  all  the  types  of  practical  dynamo  machines,  iron  arma- 
ture cores  are  employed. 

All  that  can  be  done  is  to  reduce  these  losses  as  far  as  is 
commercially  practicable.  In  the  case  of  the  iron  core,  for 


EDDY   CURRENTS.  165 

example,  the  advantage  arising  from  its  use;  namely,  the 
decrease  in  the  reluctance  of  the  magnetic  circuit,  can  be 
retained,  provided  the  material  of  the  core  is  laminated,  /.  e. , 
made  continuous  in  the  direction  of  the  magnetic  flux -paths, 
and  discontinuous  at  right  angles  to  this  direction. 

175.  If  a  piece  of  metal  be  revolved  in  a   magnetic  field,  it 
will    enclose  magnetic  flux.     A  distribution  of  E.  M.  Fs.  will 
be  established  in  it  according  to  the  rate  at  which  the  enclosure 
takes  place,  and  depending  upon  the  shape  of  the  piece.     These 
E.  M.  Fs.  will   produce  eddy  currents   in  the  moving  metal. 
The  rate   of  expending  work   in  eddy  currents  will  be,  for  a 
given  flux   intensity  in  the  metal,  in  direct  proportion  to  the 
conductivity   of  the   material.     A  piece  of   revolving   copper 
will  have  much  more  work  expended  in  it  by  eddy  currents  than 
a  piece  of  lead  or  German  silver.     If,  however,  we  divide  the 
mass  of  metal  into  a  number  of  segments  or  smaller  portions, 
the  total  E.  M.  F.   at  any  instant  will   be  divided  into  a  num- 
ber of  parts,  one  in  each   segment,  and  the  resistance  of  each 
segment  to  its  E.  M.  F.  will  be  much  greater  than  the  ratio 
of  the  resistance  of  the  entire  mass  to  the  total  E.  M.  F.  in 
such  mass.     The  energy  wasted  in  the  mass  will  therefore  be 
reduced.     For  this  reason,   the  iron  core   of  the  armature  is 
divided  into  sheets  or  laminae,  in  such  a  manner  that  the  sheets 
afford  a  continuous  path  to  the  magnetic  flux,  but  no  circuit  is 
provided  for  eddy  currents  across  the  sheets.     The  magnetic 
flux   is   conducted  through  the  entire  length  of  the  sheet,  but 
the  circuits  of  the  eddy  currents  are  all   in  the  cross-sections 
of  the  sheet.     The  division  of  the   armature  core  does  not, 
therefore,  increase  the  magnetic  resistance,  or  reluctance  of  the 
armature,   but    enormously   increases   its   resistance   to   eddy 
currents. 

176.  Fig.  146  represents  at  Z>,  an  armature  core  of  solid  iron 
capable  of  being  revolved  in  aquadripolar  field  JV1,  S1,  ^Va,  *S"3, 
the  arrows  indicating  the  general  directions  of  the  flux  paths. 
The  cross-section  of  the  armature  is  shown  at  A,  and  the  arrows 
represents  diagrammatically  the  distribution  of  the  eddy  cur- 
rents set  up  in  the  solid  mass  of  iron  during  the  rotation  of  the 
armature.     At  B,  the  cross-section  is  represented  with  lamina- 


i66 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


tions,  parallel  to  the  axis  of  the  armature,  as,  for  example,  when 
the  armature  core  is  composed  of  a  spiral  winding  of  sheet-iron 
ribbon.  Here  the  eddy  currents  are  limited  to  the  cross- 
section  of  each  band  or  lamina.  The  magnetic  flux,  however, 
has  to  penetrate  all  the  discontinuities  between  the  bands,  in 
order  to  penetrate  to  the  deepest  layer,  unless  the  flux  be 
admitted  to  the  armature  on  its  sides,  as  shown  in  Fig.  8. 

At  <7,  the  armature  is  laminated  in  planes  perpendicular  to 
the  axis,  or  is  built  up  of  sheet  discs.  Here  the  eddy  currents 
are  confined,  as  in  the  last  instance,  to  the  section  of  each  disc, 
but  the  flux  passes  directly  along  each  sheet. 

While,  therefore,  the  methods  of  construction  indicated  at 


N2 


FIG.     146. — DIAGRAM    ILLUSTRATING   EFFECTS    UPON  EDDY   CURRENTS   OF 
LAMINATING    ARMATURE   CORES. 

B  and  C,  are  equally  favorable  to  the  suppression  of  eddy 
currents,  B,  tends  to  increase  the  reluctance  of  the  armature, 
and  to  magnetically  saturate  the  outer  layers  of  the  core,  with 
a  corresponding  sparsity  of  flux  in  the  inner  layers,  except 
when  the  field  poles  cover  the  sides  of  the  armature. 


177'  Taking  a  single  lamina  of  the  armature  core,  it  is  clear 
that  if  the  intensity  in  the  core  is,  say,  12  kilogausses,  each 
square  centimetre  of  cross-section  in  the  lamina  is  linked  with 
12  kilowebers,  first  in  one  direction  and  then  in  the  opposite 
direction,  as  the  armature  moves  from  one  pole  to  the  next. 
The  value  of  the  E.  M.  F.  round  the  cross-section  of  the 
lamina,  considered  as  a  loop,  depends  upon  the  speed  with 


EDDY  CURRENTS.  167 

which  the  linkage  takes  place,  and,  therefore,  on  the  intensity 
<B  the  speed  of  rotation  and  the  number  of  poles.  The  aver- 
age E.  M.  F.  in  a  lamina,  rotating  at  a  given  speed  through  a 
quadripolar  field  of  intensity  (B  =  12,000,  would  be  four  times 
as  great  as  when  passing  through  a  bipolar  field  of  intensity 
<B  =  6,000.  The  rate  at  which  an  E.  M.  F.  of  e  volts  expends 

f 
energy  in  a  resistance  of  r  ohms,  being  —  watts,    the   average 

wasteful  activity  in  eddy  currents  depends  upon  the  square  of 
the  speed  of  magnetic  reversal  in  the  core,  and  also  upon  the 
square  of  .the  intensity.  If,  then,  we  double  the  speed  of 
revolution  in  an  armature  core,  we  quadruple  the  eddy  current 
waste  of  power.  The  higher  the  intensity  of  magnetic  flux  in 
the  armature,  and  the  more  rapid  the  reversal,  the  more 
important  becomes  the  careful  lamination  of  the  armature,  but 
the  eddy-current-loss  in  armature  cores  is  usually  very  small 
when  the  plates  have  a  thickness  not  exceeding  0.02". 

Moreover,  when  powerful  eddy  currents  are  present,  the 
M.  M.  F.  they  establish  has  such  a  direction  as  opposes  the 
development  of  magnetic  flux  by  the  field,  so  that  the  existence 
of  powerful  eddy  currents  in  an  armature  core  tends  to  shield 
the  interior  of  the  core,  or  its  laminae,  from  magnetic  flux, 
thereby  reducing  the  effective  cross-section  of  the  armature, 
or  increasing  its  apparent  reluctance.  This  effect  is  usually 
small  in  revolving  armatures  at  ordinary  speeds  of  rotation, 
but  becomes  appreciable  when  the  frequency  of  reversal  is 
high  and  the  degree  of  lamination  insufficient. 

178.  It  used  to  be  the  universal  practice  to  separate  adjacent 
sheets  of  iron  by  thin  sheets  of  paper,  when  assembling  the 
cores  of  armatures,  so  as  to  ensure  the  complete  insulation  of 
the  separate  laminae.  This  introduction  of  paper  into  the  core 
had  the  disadvantage  of  reducing  the  effective  permeance  of 
the  armature  core,  or  in  other  words,  of  increasing  the  flux 
density  in  the  iron.  It  has  been  ascertained  experimentally, 
however,  in  recent  times,  that  the  paper  could  usually  be  dis- 
pensed with,  as  the  superficial  layer  of  oxide  on  the  iron  sheets 
formed  a  layer  of  sufficient  resistance  to  effectually  insulate 
the  laminae  against  the  feeble  E.  M.  Fs.  in  the  eddy  current 
circuits. 


1 68  ELECTRO-DYNAMIC  MACHINERY, 

179.  As  we  have  seen,  eddy  currents  are  not  limited  to  the 
iron  core  of  an  armature,  but  are  also  set  up  in  the  conductors 
wound  on  the  armature. 

In  this  case,  eddy  currents  are  set  up  in  their  substance  by 
revolution  under  the  poles,  but  the  conditions  differ  slightly  in 
detail.  A  Gramme-ring  armature,  for  example,  has  no  eddy 
currents  set  up  in  the  conductors  except  upon  the  outer  sur- 
face of  the  armature,  since  the  flux  passes  through  the  wire  at 
the  outer  surface  and  not  through  the  wire  on  the  inner  sur- 
face. Similarly,  a  drum  armature  has  no  eddy  currents  set  up 
in  the  wire  upon  the  ends  of  the  drum,  if  we  may  neglect  such 
leakage  flux  as  may  pass  through  the  ends  of  the  core.  Again, 
the  amount  of  eddy-current-loss  will  depend  upon  the  distribu- 
tion of  the  magnetic  flux  over  the  surface  of  the  armature.  If 
the  flux  entering  the  armature  terminates  sharply  at  the  edge 
of  the  pole-pieces,  so  that  the  wire  suddenly  enters  or  suddenly 
leaves  a  powerful  magnetic  field  in  the  air-gap,  the  rate  of 
change  of  the  flux  enclosed  in  the  substance  of  the  wire  will 
rapidly  vary,  inducing  a  brief,  but  powerful,  E.  M.  F.  in  its 
substance,  and  the  total  expenditure  of  energy  by  eddy  cur- 
rents will  be  considerably  greater  than  if  the  gradient  of 
magnetic  intensity  in  the  neighborhood  of  the  polar  edges  is 
less  abrupt,  and  the  E.  M.  F.  smaller  in  amount  but  more 
prolonged. 

180.  The  eddy-current-loss  for  a  given  size  of  machine  is 
apt  to  be   considerably  greater  with  low  pressure  than  with 
high  pressure  armatures,  since  the  former  require  few  massive 
copper  conductors,  while  the  latter  require  many,  separately 
insulated,    conductors.      The  plan    is,    therefore,    frequently 
adopted  of  winding  low-pressure  smooth-core  armatures  with 
multiple  conductors,  each  main  conductor  being  composed  of 
a  cable  of  separately  insulated  wires.     Even  when  this  is  done, 
an  additional  precaution  is  necessary,  namely,  to  transpose  the 
conductors  or  twist  them  through  180  degrees,  halfway  across 
the  armature   surface,    in  order  to  prevent  any  pair  of  wires 
from  acting  as  a  loop  for  the  generation  of  the  E.  M.  Fs.     This 
is  illustrated  diagrammatically  in  Fig.  147,  where  the  multiple 
conductor  CC\  consisting  of  five  insulated  wires,  laid  over 
the  surface  of  the  armature  core  A  A  A  A,  is  reversed  in  the 


EDDY  CURRENTS. 


169 


centre,  so  that  the  advancing  wire  at  one  end  becomes  the  re- 
ceding wire  at  the  other,  and  vice-versa. 

It  is  sometimes  found  that  the  insertion  of  a  sheet  iron 
cylinder  of  the  form  outlined  in  Fig.  148,  closely  fitted  into 
the  polar  bore,  and  forming  a  tube  within  which  the  armature 
revolves,  greatly  diminishes  the  waste  of  energy  in  eddy 
currents.  This  is  for  the  reason  that  the  edges  of  the  pole- 
pieces  are  removed,  and  the  flux  through  the  entrefer  gradu- 
ally varies  between  zero  and  full  intensity  as  we  advance  round 
the  field.  The  effective  area  of  the  polar  surfaces  is  for  the 
same  reason  increased.  The  objection  to  the  introduction  of 
such  a  cylinder  lies  in  the  magnetic  leakage  it  introduces;  for, 


A, 


FIG.    147.  —  DIAGRAM     INDICATING   THE    TRANSPOSITION    OF    MULTIPLE 
ARMATURE   CONDUCTOR. 

if  S,  be  the  cross-section  of  the  soft  iron  sheet  in  square  centi- 
metres, the  flux  it  will  carry,  direct  from  pole  to  pole,  will  be 
roughly  20,000  S,  webers,  and  this  flux  has  to  be  provided  for 
through  the  magnetic  circuit  of  the  field  frame  in  addition  to 
other  leakage  and  the  useful  flux  through  the  armature. 


When  the  armature  conductors  are  buried  beneath  the 
surface  of  the  iron,  as,  for  example,  when  they  run  in  the  deep 
grooves  of  toothed-core  armatures,  practically  no  eddy  currents 
are  produced  in  them,  for  the  reason  that  the  space  they  oc- 
cupy is  almost  free  from  the  flux  established  by  the  field.  A 
toothed-core  armature  may,  therefore,  be  considered  as  an 
armature  in  which  the  eddy  currents  are  confined  to  the  iron 
laminae  of  the  core.  This  feature  constitutes  one  of  the 
advantages  of  toothed-core  armatures. 

182.  Besides  the  eddy  currents  set  up  in  the  armature,  and 
in  the  conducting  masses  of  the  metal  on  the  armature,  they 
also  occur  in  the  edges  of  the  pole-pieces  of  the  field  magnets, 


17°  ELECTRO-DYNAMIC  MACHINERY. 

both  in  the  case  of  dynamos  and  motors.  The  strength  of 
these  eddy  currents  is  greater  in  the  pole  which  is  approached 
by  a  generator  armature,  and  in  that  which  is  receded  from  by 
a  motor  armature,  as  is  evidenced  by  the  fact  often  observed, 
that,  although  both  polar  edges  become  warm  during  the  action 
of  the  machine,  one  edge  becomes  warmer  than  the  other. 
The  reason  for  this  difference  will  be  considered  later. 

183.  The  tendency  to  the  development  of  eddy  currents  in 
pole-pieces  is  increased  when  the  armature  is  changed  from  a 
smooth  core  to  one  of  the  toothed-core  type.  The  reasons  for 
this  are  twofold;  in  the  first  place,  in  the  toothed-core  arma- 


FIG.  148. — IRON   CYLINDER  OR  BUSHING  FOR  FIELD   CORE. 

ture  the  armature  is  brought  nearer  to  the  pole  face,  so  that 
all  magnetic  disturbances  in  the  armature  are  more  likely  to 
set  up  corresponding  disturbances  in  the  poles;  in  the  second 
place,  because  the  revolving  teeth  set  up  waves  of  magnetiza- 
tion in  the  polar  surfaces,  thus  giving  rise  to  the  development 
of  eddy  currents.  Consequently,  the  change  from  a  smooth- 
core  to  a  toothed-core  armature  suppresses  the  eddy  cur- 
rents in  the  wire  on  the  armature,  but  creates,  or  tends  to 
create,  eddy  currents  in  the  pole-pieces. 

184.  In  some  types  of  machines  the  pole-pieces  are  grooved 
or  slotted,  so  as  to  check  the  development  of  eddy  currents, 
just  as  the  armature  is  in  effect  grooved  or  slotted  by  the  use 
of  laminated  cores.  An  example  of  this  is  seen  in  Fig.  14.  In 
fact,  some  field  magnets  are  constructed  of  a  frame  of  cast  iron 
or  cast  steel,  with  receptacles  within  which  are  placed  the  pole- 


EDDY  CURRENTS.  171 

pieces  formed  of  a  number  of  iron  plates  bolted  together,  the 
laminations  extending  in  the  same  direction  as  those  in  the 
armature  beneath. 

It  will  be  evident  that  there  can  be  no  tendency  to  set  up 
eddy  currents  in  the  solid  cores  of  the  field  magnets  excited 
by  steady,  continuous  currents.  Consequently,  no  advantage 
is  derived  from  a  lamination  of  field  magnet  cores  at  distances 
beyond  the  influence  of  magnetic  changes  produced  by  the 
teeth  or  conductors  on  the  revolving  armature. 


CHAPTER  XVII. 

MAGNETIC     HYSTERESIS. 

185.  Besides  the  losses  in  the  iron  masses  of  a  dynamo  due 
to  eddy  currents,  there  are  others  in  the  same  masses  due  to 
magnetic  friction  or  hysteresis.     These    latter  losses,   like   the 
others,  are  dissipated  as  heat. 

The  losses  due  to  hysteresis  occur  in  nearly  all  forms  of 
dynamo-electric  machinery.  In  continuous-current  generators 
these  losses  are  practically  limited  to  the  armature;  in  some 
forms  of  alternating-current  machines,  they  exist  both  in  the 
armature  and  field,  and  are  especially  present  in  alternating- 
current  transformers.  It  becomes,  therefore,  a  matter  of  no 
little  importance  to  thoroughly  understand  the  nature  of  this 
source  of  loss. 

186.  A  certain  amount  of  energy  has  to  be  expended  in 
order  to  magnetize  a  bar  of  iron.     This  energy  resides  in  the 
magnetic  flux  passing  through  the  magnetic  circuit  of  the  bar. 
The  energy  is  transferred  from  the  magnetizing  circuit  by  the 
production    of   a  C.   E.  M.  F.    in  the  magnetizing    coil,    and 
this  C.   E.    M.    F.  e,   (usually   very  small),    multiplied  by    the 
magnetizing  current  strength  7,  at  that  moment,  gives  as  the 
product  e  7,  the  activity  expended  in  producing  the  magnetic 
field.     As  soon  as  the  full  magnetic  flux  is  established,  the 
C.    E.    M.     F.  ceases,   being    dependent    upon    the    rate    of 
change  of  flux  enclosed,  so  that  no  more   energy  is  expended 
in  the  iron,  and  the  current  only  expends  energy  as  /  V,  in  heat- 
ing the  magnetizing  coil.     When  the  magnetizing  current  is 
interrupted,  say  by  short  circuiting  the  source  of  E.  M.  F.  in  the 
circuit,  the  magnetism  in  the  bar  tends  to  disappear,  and,  as 
the  magnetic  flux  diminishes,  an  E.  M.  F.  is  set  up  in  the  coil, 
tending  to  prolong  the  action  of  the  waning  magnetizing  cur- 
rent.    In  other  words,  the  E.  M.  F.   set  up  in  a  circuit  by  the 
waning  magnetic  flux  is  such  as  will   tend  to  do  work  on  the 


MAGNETIC  HYSTERESIS.  173 

current,  with  an  activity  of  the  type  e  i  watts,  and,  in  this 
manner,  restore  to  the  circuit  the  energy  expended  in  the 
magnetization.  Were  all  the  energy  in  this  case  returned  to 
the  circuit,  there  would  be  no  loss  by  hysteresis.  As  a  matter 
of  fact,  however,  while  practically  all  such  energy  would  be 
returned  to  the  circuit,  if  the  coil  magnetized  air,  wood,  glass, 
etc.,  yet,  when  the  coil  magnetizes  iron,  although  a  greater 
magnetic  flux  is  obtained,  yet  some  of  the  energy  is  not 
restored,  but  is  expended  in  the  iron  as  heat. 

187.  It  is  now  generally  believed  that  each  of  the  molecules 
in  a  mass  of  iron  is  naturally  and  permanently  magnetized,  so 
that  each  molecule  may,  therefore,  be  regarded  as  a  molecular 
compass    needle.     In    the    ordinary  unmagnetized   or  neutral 
condition  of  iron,   these   separate  molecular  magnets  possess 
no    definite    alignment,    and,     consequently,     neutralize     one 
another's  influence  by  forming  closed  loops  or  chains.     When 
the  iron  becomes  magnetized  by  subjection   to  a  magnetizing 
force,  these  loops  break  up  and -become  polarized  or  aligned, 
all  pouring  their  magnetic  flux  in  the  same  direction;    /  ^., 
parallel  to  the  magnetic  axis.     When  the  magnetizing  force  is 
removed,    the    molecular  magnets   tend    to    resume   their  old 
positions;  and,  if  they  did  resume  exactly  their  old  positions, 
the   magnetism  in  the  iron  would  entirely  disappear  on  the 
removal  of  the  magnetizing  force,  and  all  the  magnetic  energy 
would  be  restored  to  the  circuit.     In  point  of  fact,  however, 
they  do  not  exactly  resume  old  positions,  but  take  new  inter- 
mediate  positions,   by  virtue   of   which  a   certain   amount  of 
residual  magnetism  is  left  in  the  bar. 

188.  When    now   the    magnetizing    force    is   reversed,   by 
reversing  the  current  through  the  magnetizing  coil,  the  mole- 
cules  are    forced  around,  and  breaking  suddenly  from  their 
positions,  fall   into  new  positions,  either  with  oscillations,  or 
with    a   frictional    resistance    to    the    motion,  that  dissipates 
energy  as  heat.     The  energy  thus  lost  by  molecular  vibration 
or  molecular  friction  cannot  be  returned  to  the  circuit.     Conse- 
quently, a  loss  of  energy  occurs  in  the  circuit  supplying  the 
reversing  magnetizing  force,  at  each  reversal  of  magnetism  in 
the  magnetized  iron,  since  the  opposing  E.  M.  Fs.   developed 


174  ELECTRO-DYNAMIC  MACHINERY 

in  the  coil  during  magnetization  and  demagnetization  are  not 
equal,  and  the  energy  so  lost  results  in  an  increase  in  tempera- 
ture of  the  iron.  By  hysteresis,  (his-ter-ee'-sis),  is  meant  that 
property  of  iron,  or  other  magnetic  metal,  whereby  it  tends  to 
resist  changes  in  its  magnetization  when  subjected  to  changes 
in  magnetizing  force.  That  is  to  say,  when  a  mass  of  iron  is 
successively  magnetized  and  demagnetized,  or  passes  through 
cycles  of  magnetization,  the  magnetic  intensity  in  the  mass  lags 
behind  the  impressed  magnetizing  force.  The  word  hysteresis 
take  its  origin  from  this  fact,  since  it  is  derived  from  a  Greek 
word  meaning  to  lag  behind.  This  phenomenon  is  called  hys- 
teresis, and  the  loss  of  energy  due  to  this  cause  is  called 
hysteretic  loss,  or  loss  of  energy  by  hysteresis. 

189.  When  iron  undergoes  successive  magnetic  reversals,  the 
amount  of  hysteretic  loss  is  found  to  depend  upon  the  maximum 
magnetic  intensity  in  the  iron  at  each  cycle;  that  is  to  say, 
upon  the  maximum  value  of  (B.  As  (B,  increases,  the  amount 
of  work  that  has  to  be  expended  in  reversing  the  magnetization 
increases,  and  if  we  double  the  value  of  (B,  we  practically 
treble  the  amount  of  work  that  has  to  be  expended.  It  was 
first  pointed  out  by  Steinmetz,  as  a  consequence  of  this  rela- 
tion, that  the  hysteretic  loss  varied  as  the  i.6th  power  of  (B,  or 
as  (B  1>e,  the  formula  for  the  amount  of  activity  expended  in 
one  cubic  centimetre  of  magnetic  metal  being  P  =  n  rj  (B  '•* 
watts.  Since  the  same  loss  of  energy  occurs  in  a  cubic  centi- 
metre during  each  cycle,  the  more  rapidly  the  cycles  recur, 
the  greater  will  be  the  wasteful  activity,  and  ;/,  in  the  above 
formula,  expresses  the  number  of  complete  cycles  through 
which  the  iron  is  carried  per  second.  The  coefficient  77,  is  the 
hysteresis  coefficient  for  the  metal  considered,  and  has  to  be  de- 
termined experimentally.  It  may  be  regarded  as  the  activity 
in  watts  which  would  be  expended  in  one  cubic  centimetre 
of  the  metal  when  magnetized  and  demagnetized  to  a  flux 
density  of  one  gauss  at  one  complete  cycle  or  double  rever- 
sal per  second.  The  following  table  gives  the  values  of  this 
coefficient,  and  also  the  amount  of  hysteretic  loss  produced  in 
a  cubic  centimetre,  and  in  a  pound,  of  ordinary  good  com- 
mercial sheet  iron  at  various  frequencies  and  intensities. 


MAGNETIC  HYSTERESIS. 


'75 


Table  Showing  the  Hysteritic  Activity  in  Good ',  Soft  Sheet  Iron  or  Steel  Undergoing  One 
Complete  Magnetic  Cycle  per  Second,  in  Watts  per  Cubic  Centimetre,  Watts  per  Cubic 
Inch,  and  Watts  per  Pound,  for  Various  Magnetic  Intensities  in  Gausses  and  in 
Webers  Per  Square  Inch. 


Webers,    per 
sq.  in  

6,452 

12,900 

19,360 

25,8lO 

32,260 

38,710 

45,160 

51,620 

58,060 

Gausses[(BJ.        1,000 

2,000 

3,000 

4,OOO 

5,OOO 

6,000 

7,000 

8,000 

9,000 

Watts,  per  cc. 

—8 
1.58X10 

-6 
4.78x10 

-5 
9.I5XIO 

-4 
1.45X10 

-4 
2.07X10 

-4 
2.78X10 

-4 
3-55X10 

-4 
4.40X10 

-4. 
5-31x10 

Watts,      per 
cubic  in.  .  . 

-4 
2.59X10 

-4 

7.84X10 

-3 
I.50XIO 

2.38x10 

—3 

3.40X10 

—3 

4-55X10 

-3 
5.82X10 

-3 

7-20X10 

-3 

8.60JIIO 

Watts,  per  lb. 

-4 
9.17X10 

-3 

2.78x10 

-3 
5.32X10 

-3 
8.43X10 

-2 
1.  21X10 

-2 
I.62XIO 

-2 
2.06X10 

-a 

2.56x10 

-2 

3.09X10 

Webers,   per 
sq.   in  ...    . 

64,520 

70,960 

77,420 

83,860 

90,320 

96,770 

103,200 

109,700 

Il6,IOO 

Gausses  [(B]. 

10,000 

II,OOO 

12,000 

13,000 

14,000 

15,000 

l6,000 

17,000 

18,000 

Watts,  per  cc. 

-4 
6.28X10 

-4 
7-3IXIO 

-4 
8.40X10 

-4 

9-55X10 

-3 

I.OSXIO 

-3 
1.  20X10 

—3 
I.33XIO 

-3 

I.47XIO 

-3 

1.61x10 

Watts,      per 
cubic  in  ... 

-2 

1.03X10 

-2 
I.2OXIO 

-2 
1.38x10 

—2 
I.57XIO 

-2 

1.76x10 

-2 
I.97XIO 

-2 
2.I8XIO 

—9 
2.4IXIO 

-2 
2.64X10 

Watts,  per  lb. 

-2 
3.65X10 

-2 
4.25X10 

-2 

4.89X10 

-» 
5.56x10 

-2 

6.26X10 

-2 

6.79X10 

-2 

7.75X10 

-2 

8.53XTO 

-2 
9.35X10 

IpO.  As  an  example  of  the  hysteretic  activity,  we  may  con- 
sider a  pound  of  iron  subjected  to  a  periodic  alternating  flux 
density  of  ten  kilogausses,  with  a  frequency  of  25  cycles-per 
second.  From  the  preceding  table,  it  is  seen  that  at  10  kilo- 
gausses  the  hysteretic  activity  is  0.0365  watts-per-pound,  at  a 
frequency  of  one  cycle  per  second.  At  25  cycles  per  second 
this  would  be  25  x  0.0365  =0.9125  watt  =  0.9125  joule-per- 
second  =  0.6735  foot-pound  per  second.  Consequently  the 
hysteretic  activity  might  be  represented  by  lifting  the  pound  at 
the  rate  of  0.6735  foot  Per  second  against  gravitational  force. 
If,  therefore,  all  the  iron  in  an  armature  core  be  subjected  to 
an  intensity  of  ten  kilogausses,  and  rotates  25  times  per  second 
in  a  bipolar  field,  12.5  times  per  second  in  a  quadripolar  field, 


176  ELECTRO-DYNAMIC  MACHINERY. 

or  6.25  times  per  second,  in  an  octopolar  field,  hysteretic 
activity  is  being  expended  at  a  rate  which  is  probably  repre- 
sented by  the  activity  of  raising  the  whole  armature  core  about 
eight  inches  per  second. 

It  is  to  be  observed  that  the  table  represents  average  samples 
of  good  commercial  iron,  and  by  no  means  the  best  quality  of 
iron  obtainable. 

191.  As  an  example  of  the  application  of  this  table,  suppose 
that  it  is  required  to  estimate  the  power  expended  in  hysteresis 
during  the  rotation  of  the  armature  of  the  octopolar  generator 
represented  in  Fig.  129,  the  weight  of  iron  in  the  armature 
being  2,700  Ibs. 

At  the  maximum  intensity  of  9,500  gausses,  or  61,290  webers- 
per-sq.  in.,  the  table  shows  that  the  hysteretic  activity  per 
pound  at  one  cycle  per  second  is  about  3.4  X  io~a  watts.  In 
each  revolution  of  the  armature  there  would  be  eight  reversals, 
.  or  four  complete  cycles,  and  at  2.867  revolutions  per  second, 
the  frequency  of  reversal  would  be  11.468  cycles  per  second. 
The  total  hysterettc'activity  is,  therefore, 

P  X  2,700  X  3-4  X  io~a  X  11.468  =  1,053  watts. 

This  would  be  the  hysteretic  activity  in  the  armature  when 
generating  155.7  volts.  When  generating  a  lower  E.M.F.,  the 
flux  intensity  in  the  armature  would  be  reduced,  and,  therefore, 
the  hysteretic  activity. 

192.  Hysteresis,    therefore,   occurs   when  a   mass    of  iron 
undergoes  successive   magnetizations   and    demagnetizations, 
and  this  is  true  whether  such  are  caused  by  the  reversal  of  the 
magnetizing  current,  with  the  mass  at  rest,  or  by  the  reversal  of 
the  direction  of  the  mass  in  a  constant  magnetic  field.     Conse- 
quently, the  revolutions  of  the  armature  of  a  dynamo  or  motor, 
occasioning   the   successive  magnetizations   and    demagnetiz- 
ations of  its  core,  are  accompanied  by  an  hysteretic  loss  of 
energy. 

The  amount  of  this  hysteretic  loss  increases  directly  with  the 
volume  V,  of  iron  in  the  armature  in  c.  c.,  the  number  «,  of 
revolutions  of  the  armature  per  second,  the  hysteretic  coeffi- 
cient ff  of  the  iron  employed,  and  the  i.6th  power  of  the 
maximum  magnetic  intensity  in  the  iron;  for,  it  is  evident  that 


XTNIVERSITT) 
MAGNETIC  H  YSTERESI3£*Q^\       177 


in  one  complete  revolution  of  the  armature  its  direction  of 
magnetization  will  have  undergone  two  reversals,  provided  that 
the  field  is  bipolar.  In  a  multipolar  field  the  number  of  revers- 
als increases  with  the  number  of  poles/,  and  the  hysteretic 

activity  becomes  P  =  —  nrl  r  -  watts.     In  the  case  of  a  gen- 

erator, this  activity  must  be  supplied  by  the  driving  power, 
and  in  the  case  of  a  motor  by  the  driving  current. 

IQ3-  When  a  generator  armature  is  at  rest  in  an  unmagnet- 
ized  field,  the  torque;  i.  e.,  the  twisting  moment  of  the  force 
which  must  be  applied  to  the  armature  in  order  to  rotate  it,  is 
such  as  will  overcome  the  friction  of  the  journals  and  brushes. 
When,  however,  the  field  is  excited,  so  that  the  armature 
becomes  magnetized,  the  torque  which  is  necessary  to  rotate 
the  armature  is  increased,  even  when  the  armature  is  symmet- 
rically placed  in  regard  to  the  poles.  This  extra  torque  is  due 
to  hysteresis.  It  is  sometimes  called  the  hysteretic  torque,  and 
is  equal  to 

V  77  /(B  1'8 
t  =  —  —  --  megadyne-decimetres. 

194.  The  total  useless  expenditure,  therefore,  of  power  in  an 
armature  core  is  the  sum  of  the  hysteretic  and  eddy  current 
loss.     The  former  increases  as  the  speed  of  revolution  directly, 
but  the  latter,  as  already  pointed  out,  increases  as  the  square 
of  the  speed.     Consequently,  if  we  have  an  unwound  armature 
core,  and  rotate  it  on  its  shaft  through  a  field  which  is  at  first 
unexcited,  we  expend  an  activity  which  might  be  measured,  and 
which  would  be  entirely  frictional  loss.     When  the  field   is  ex- 
cited, we  expend  activity  against  mechanical  friction,  hysteresis 
and  eddy  currents  combined.     By  varying  the  speed  of  rotation, 
and  observing  the  rate  at  which  the  activity  given  to  the  rotat- 
ing armature  increases,   it  is  possible  to  separate   the  three 
descriptions  of  losses  from  each  other. 

195.  Although,  as  we  have  seen,  the  hysteretic  loss  increases 
with  the  i.  6th  power  of  the  intensity  of  flux,  yet  it  is  stated  to 
have  been  found  experimentally,  that  when  a  mass  of  iron,  such 
as  an  armature,  is  rotated  in  a  sufficiently  powerful  magnetic 


178  ELECTRO-DYNAMIC  MACHINERY. 

field,  the  hysteretic  loss  entirely  disappears,  owing  to  the  sup- 
posed rotation  of  all  the  elementary  molecular  magnets  about 
their  axes  during  the  rotation  of  the  armature  without  losing 
parallelism,  and,  consequently,  without  any  molecular  oscil- 
lation and  expenditure  of  magnetic  energy  as  heat.  So  far 
as  experiments  have  yet  shown,  this  critical  intensity  in  the 
iron  is  above  that  which  ordinary  dynamo  or  motor  armatures 
attain,  so  that  under  practical  conditions,  the  i.6th  power  of 
the  maximum  intensity  determines  the  hysteretic  loss. 

196.  From  an  examination  of  the  formula    expressing  the 
hysteretic  activity  in  the  armature,    it   is    evident  that    the 
activity  might  be  decreased  by  a  decrease  either  in  the  number 
of  poles,  the  speed  of  revolution,  the  flux  density,  or  the  hys- 
teretic coefficient.     Since,  however,  in  any  machine  the  first 
three  factors  are   practically  fixed,   it  is  important  that   the 
remaining  factor,  or  hysteretic  coefficient,  should   be  kept  as 
low  as  is  commercially  possible.     For  this  reason,  whenever 
the  hysteretic  loss  is  a  considerable  item  in  the  total  losses  of 
the  generator,  care  is  taken  to  select  the  magnetically  softest 
iron  commercially  available,  in  which  the  hysteretic  coefficient 
is  a  minimum. 

197.  We  have  already  referred  to  the  increase  in  tempera- 
ture of  the  edges  of  the  field-magnet  poles  during  the  operation 
of  a  dynamo  armature,  and   have  ascribed  the  cause  of  such 
heating  to  the  development  of  eddy  currents  locally  produced 
there.     It  is  to  be  remarked,  however,  that  some  of  the  heat 
in  such  cases  may  usually  be  ascribed  to  true  hysteretic  changes 
in  magnetization. 


CHAPTER  XVIII. 

ARMATURE    REACTION    AND    SPARKING    AT    COMMUTATORS. 

198.  In  the  operation  of  a  dynamo-electric  generator,  con- 
siderable difficulty  is  frequently  experienced  from  the  sparking 
which  occurs  at  the  commutator,  that  is  to  say,  instead  of  the 
current  being  quietly  carried  off  from  the  armature  to  the 
external  circuit,  a  destructive  arc,  which  produces  burning, 
occurs  between  the  ends  of  the  brushes  and  the  commutator 
segments.  The  tendency  of  this  sparking,  unless  promptly 
checked,  is  to  grow  more  and  more  marked  from  the  mechani- 
cal irregularities  produced  by  the  pitting  and  uneven  erosion 


FIG.    149. — GRAMME-RING    ARMATURE    IN    BIPOLAR    FIELD   ON   OPEN   CIRCUIT. 

of  the  commutator  segments.  It  becomes,  therefore,  a  matter 
of  considerable  practical  importance  to  discuss  the  causes  of 
sparking  at  the  commutator,  and  the  means  which  have  been 
proposed,  and  are  in  use,  to  overcome  the  difficulty. 

Ipp.  When  a  Gramme-ring  armature,  such  as  that  shown  in 
Fig.  149,  is  rotated  on  open  circuit,  in  a  uniform  bipolar  field, 
the  brushes,  when  placed  on  the  commutator,  must  be  kept  at 
diametrically  opposite  points  corresponding  to  the  line  n  n. 
If  applied  to  the  commutator  at  any  other  points,  sparking  will 
probably  occur,  although  the  armature  is  on  open  circuit. 
The  reason  for  this  is  seen  by  an  examination  of  the  figure, 
which  represents  a  pair  of  coils  C,  C,  about  to  undergo  com- 

179 


i8o 


ELECTRO-DYNAMIC  MACHINERY. 


mutation  ;  i.  e.,  about  to  be  transferred  by  the  rotation  of  the 
armature  from  one  side  of  the  brush  to  the  other,  and  being 
short  circuited  by  the  brushes,  as  they  bridge  over  the  adjacent 
segments  of  the  commutator  to  which  their  ends  are  connected. 
Since  the  coils  C,  C',  in  the  position  shown,  embrace  the 
maximum  amount  of  flux  passing  through  the  armature,  there 
will  be  no  E.  M.  F.  induced  in  them,  and,  consequently,  there 
will  be  no  current  set  up  during  the  time  of  short  circuit  under 
the  brushes.  In  other  words,  the  prime  condition  for  non- 
sparking  at  the  commutator  is  that  the  coils  shall  be  short 


FIG.    150. — GRAMME-RING     ARMATURE    WITH    BRUSHES    DISPLACED   FROM 
NEUTRAL   LINE. 

circuited   only  at  the    time,   and    in   the   position,   where  no 
E.  M.  Fs.  are  being  generated  in  them. 

200.  If  the  brushes  be  advanced  into  a  position  such  as  that 
represented  in  Fig.  150,  so  that  the  diameter  of  commutation  : 
i.  e.,  the  diameter  of  the  commutator  on  which  the  brushes  rest, 
is  shifted  from  B,  B ',  to  a  new  position,  powerful  sparking  will, 
probably,  be  set  up,  for  the  reason  that  in  this  position  the 
rate  of  change,  in  the  flux  linked  with  these  coils,  is  consider- 
able, and,  consequently,  there  is  a  considerable  E.  M.  F. 
induced  in  them,  so  that,  when  they  are  short  circuited  by  the 
brushes,  heavy  currents  tend  to  be  produced  in  the  circuit  of 
these  coils  according  to  Ohm's  law.  If,  for  example,  a  bipolar 
Gramme-ring  armature  gives  passage  to  a  total  useful  flux  of 
i  megaweber,  and  there  are  1,000  turns  on  the  armature, 
and  50  segments  in  the  commutator,  then,  if  the  speed  of  rota- 
tion be  10  revolutions  per  second,  the  E.  M.  F.  set  up  between 
the  brushes  will  be 


10  X  1,000  x  1,000,000 
100,000,000 


=    IOO 


volts, 


ARMATURE   REACTION.  l8r 

and,  since  there  are  25  commutator  bars  on  each  side  of  the 
diameter  of  commutation,  there  will  be  an  average  of  four 
volts  per  coil  of  20  turns.  If  the  resistance  of  each  coil  be 
o.oi  ohm,  the  current  which  tends  to  be  set  up  in  a  short- 
circuited  coil  having  the  average  E.  M.  F.  is 

4 

=  400  amperes. 


o.oi 

201.  It   now   remains   to   be   explained   how  the   existence 
of  a  powerful  current  in   the  short-circuited  coil  will  produce 
violent  sparking  at  the  commutator.     It  is  well  known  that 
the   presence  of  a  spark  indicates  a  higher  E.  M.  F.  than  the 
four  volts,  which  we   have  assumed  in   this  case  is  to  be  gen- 
erated in  the  short-circuited  coil.     The  increase  in  the  voltage 
at  the  moment  of  sparking  is  due  to  what  is  called  the  induct- 
ance  of  the  coil. 

At  the  moment  of  short  circuiting  the  coil  by  the  bridging  of 
the  brushes  across  the  two  adjacent  commutator  segments,  a 
powerful  magnetic  flux  is  set  up  in  the  coil,  owing  to  its  M.  M.  F. 
This  flux  is  so  directed  through  the  coil  as  to  set  up  in  it  an 
E.  M.  F.  which  opposes  the  development  of  the  current.  On 
the  cessation  of  the  current,  owing  to  the  breaking  of  the  coil's 
circuit  at  the  commutator,  the  coil  is  rapidly  emptied  of  flux, 
and  a  powerful  E.  M.  F.  is  set  up  in  the  same  direction  as  the 
current,  sufficiently  powerful  to  produce  sparking  between  the 
brush  and  the  edge  of  the  segment  it  is  leaving.  The  E.  M.  F. 
so  generated  during  the  filling  or  emptying  of  the  loop  by  its 

own  flux  is  called  the  E.  M.  F.  of  self-induction. 

f=j 

202.  Fig.  151  diagrammatically  represents  the  flux  produced 
in  the  short-circuited  coils  C',  C,  by  the  M.  M.  F.  of  the  current 
produced    during   the  short  circuit.     This  flux  passes  princi- 
pally through  the  air-gap  and  neighboring  pole  face,  a  small 
portion  passing  through  the  air  in  the  interior  of  the  armature 
between  the  core  and  the  shaft.     The  greater  the  flux  produced 
by  the  coil,  the  greater  will  be  the  E.  M.  F.  developed  in  the 
coil,  when   the  flux  is  suddenly  withdrawn.      The    capability 
of  a  conducting  loop  or  turn  for  producing  E.  M.  F.  by  self- 
induction  is  called   its  inductance,  and  may  be   measured  by 
the  linkage  of  flux  with  the  turn  per  ampere  of  the  current  it 
carries,  that  is,  by  the  amount  of  flux  passing  through  it. 


1 82  ELECTRO-DYNAMIC  MACHINERY. 

203.  We  have  thus  far  considered  the  coils  C,  C ',  as  being 
composed  of  a  single  turn.  If,  however,  each  of  these  coils  is 
composed  of  two  turns,  and  the  same  current  strength  passes 
through  each  of  these  turns,  then  the  M.  M.  F.  of  the  coil  will 
be  doubled,  and,  if  the  iron  in  the  armature  core  and  pole 
face,  is  far  from  being  saturated,  the  amount  of  flux  passing 
through  the  two  turns  will  be  twice  as  great  as  that  which  pre- 
viously passed  through  one.  When  this  flux  is  introduced  or 
removed  it  will  generate  E.  M.  F.  in  both  turns,  and,  conse- 
quently, will  induce  twice  as  much  E.  M.  F.  in  the  two  turns 
together  as  in  a  single  turn.  The  inductance  of  the*  coil,  or  its 
capacity  for  developing  E.  M.  F.  by  self-induction,  is  thus  four 
times  as  great  with  two  turns  as  with  one,  because  there  is 


FIG.   151. — DIAGRAMMATIC   REPRESENTATION   OF   FLUX   IN   MAGNETIC    CIRCUIT 
OF    SHORT-CIRCUITED    COIL. 

double  the  amount  of  flux,  and  double  the  number  of  turns 
receiving  that  flux. 

204.  It  is  evident,  therefore,  that  the  inductance  of  a  coil 
increases  rapidly  with  the  number  of  its  turns,  and  although 
not  quite  proportionally  to  the  square  of  the  number,  since, 
with  a  large  number  of  turns,  although  the  M.  M.  F.  is  in- 
creased in  proportion  to  the  number,  yet  the  amount  of  flux 
passing  through  each  of  the  turns,  owing  to  leakage,  is  not  the 
same.  The  E.  M.  F.  of  self-induction  generated  in  each  coil 
depends: 

(i.)  Upon  the  E.  M.  F.  induced  in  the  coil  by  the  revolution 
of  the  armature. 

(2.)  Upon  the  resistance  of  the  coil,  or  its  capability  for 
allowing  a  large  current  to  flow  through  it. 

(3.)  Upon  the  inductance  of  the  coil,  or  its  capability  for 


ARMATURE   REACTION.  183 

permitting  that  current  to  induce  a  powerful  E.  M.  F.  when  the 
circuit  is  made  or  broken. 

The  E.  M.  F.  induced  on  making  the  circuit  at  the  commu- 
tator is  advantageous,  since  it  checks  the  development  of  the 
current  ;  the  E.  M.  F.  induced  on  breaking  the  circuit  is 
harmful,  since  it  enables  a  spark  to  follow  the  brush. 

If,  therefore,  no  sparking  is  to  occur  in  a  dynamo-electric 
machine  at  no  load,  the  brushes  must  rest  on  segments,  con- 
nected with  coils  in  which  no  E.  M.  F.  is  being  generated. 

205.  If  the  external  circuit  of  the  armature  be  closed 
through  a  resistance,  so  that  current  flows  through  the  arma- 
ture coils  and  brushes  into  the  external  circuit,  the  preceding 
conditions  become  considerably  modified. 

Fig.  152  represents  the  condition  of  affairs  in  which  a  current 


FIG.    152. — DIAGRAMMATIC     REPRESENTATION    OF     MAGNETIC     CIRCUIT    OF 

ARMATURE. 

is  flowing  through  the  armature  coils,  and  the  brushes  are 
resting  on  the  commutator,  with  the  diameter  of  commutation 
at  the  neutral  points,  or  in  a  plane  at  right  angles  to  the  polar 
axis. 

In  this  figure  the  direction  of  the  armature  rotation  is  the 
same  as  shown  in  previous  figures;  namely,  counter-clockwise. 
Here  the  flux  produced  by  the  M.  M.  F.  of  the  armature  coils 
takes  place  in  the  circuits  digrammatically  indicated  by  the 
curved  arrows.  The  magnetization,  therefore,  produced  by 
the  current  circulating  in  the  armature  turns,  is  a  cross  mag- 
netization^ or  a  magnetization  at  right  angles  to  the  magnetiza- 
tion set  up  by  the  field  flux.  The  field  flux  through  the  poles 
and  armature  is  diagrammatically  indicated  in  Fig.  153,  where 
the  north  pole  is  assumed  to  be  situated  at  the  left-hand  side 


1 84 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


of  the  figure,  and  the  average  direction  of  the  field  flux  is  at 
right  angles  to  the  average' direction  of  the  armature  flux.  An 
inspection  of  Figs.  152  and  153  will  show  that  at  the  leading 
edges  of  the  pole-piece,  Z,  Z',  that  is,  at  those  edges  of  the  pole- 
piece  which  the  armature  is  approaching,  the  direction  of  the 
flux  produced  by  the  armature  is  opposite  to  that  of  the 


FIG.    153. — DIAGRAMMATIC   REPRESENTATION    OF   FIELD    FLUX    PASSING 
THROUGH    ARMATURE. 

flux  produced  by  the  field,  and  that,  consequently,  the  effect 
of  superposing  these  fluxes  is  to  weaken  the  flux  at  the  leading 
edge  as  is  shown  in  Fig.  154.  On  the  contrary,  at  \h^  following 
edges  F'  and  Ft  of  the  pole-pieces,  the  direction  of  the  armature 


FIG.   154. — EFFECT   OF    SUPERPOSING   ARMATURE    FLUX   ON   FIELD   FLUX. 

flux  coincides  with  the  direction  of  the  field  flux,  and  the  super- 
position of  these  two  fluxes  will  have  the  effect  of  intensifying 
the  flux  at  the  following  edges.  Consequently,  the  neutral  line 
in  the  armature,  or  the  line  symmetrically  disposed  as  regards 
the  entering  and  leaving  flux,  will  no  longer  occupy  the  posi- 
tion N,  N,  at  right  angles  to  the  polar  axis,  but  will  occupy  a 
position  n  n' ;  therefore,  in  order  to  set  the  brushes  so  that 
they  may  rest  upon  commutator  segments  connected  with  coils 


ARMATURE  REACTION.  185 

having  no  E.  M.  F.  generated  in  them,  it  is  necessary  to  bring 
the  diameter  of  commutation  into  coincidence  with  the  neutral 
line,  or  to  give  the. brushes  a  lead;  i.  e.,  a  forward  motion,  or 
in  the  direction  in  which  the  armature  is  rotating. 

206.  This,  however,  will  not  in  itself,  as  a  rule,  prevent 
sparking,  for  the  reason  that  induced  E.  M.  Fs.  are  produced 
in  the  coil  under  commutation  at  load,  even  although,  the  coil 
being  commuted  has  no  resultant  E.  M.  F.  set  up  by  rotation. 
This  induced  E.  M.  F.  is  due  to  the  inductance  of  the  coil  and 


FIG.    155. — REVERSAL   OF   CURRENT    IN   ARMATURE    COILS    DURING    COM- 
MUTATION. 

to  the  load  current  which  it  carries.  An  inspection  of  Fig.  155 
will  show  that  as  the  coil  C,  approaches  the  brush  B,  the  current 
in  the  coil,  as  shown  by  the  arrows,  is  directed  upward  on  the 
side  facing  the  observer;  while  on  leaving  the  brush,  after 
having  undergone  commutation,  the  current  in  the  coil  will  be 
flowing  in  the  opposite  direction  or  downward.  The  sudden 
reversal  of  the  current  in  the  coil  under  commutation  produces 
a  sudden  reversal  of  the  magnetic  flux  linked  with  the  local 
magnetic  circuit  of  that  coil,  and  this  sudden  change  in  the 
magnetic  flux  through  the  coil  induces  in  it  a  powerful  E.  M.  F., 
causing  a  spark  to  follow  the  brush. 

In  order  that  no  spark  shall  be  produced  from  this  cause,  it 
is  necessary  that  before  the  brush  leaves  the  segment  the  cur- 
rent in  the  coil  shall  have  become  reversed,  and  will  therefore 
be  flowing  in  the  same  direction  as  that  which  will  pass  through 
it  during  its  passage  before  the  pole  face  N.  In  order  to  effect 
this  it  is  necessary  to  bring  the  coil  that  is  being  commutated 
into  a  field  of  sufficient  intensity  to  induce  in  it,  while  short 
circuited,  a  current  strength  equal  and  opposite  to  that  which 


186  ELECTRO-DYNAMIC  MACHINERY. 

passes  when  it  first  becomes  short  circuited  by  the  brush.  It 
is  not,  therefore,  usually  possible  to  keep  the  brushes  on  the 
neutral  line  as  shown  in  Fig.  154,  at  n  n',  but  their  lead  must 
be  increased,  until  the  coil  under  commutation  is  in  a  sufficiently 
powerful  field  beneath  the  pole  face  to  produce,  or  nearly  pro- 
duce, this  reversal  of  current.  The  amount  of  lead  necessary 
to  give  to  the  brushes  in  order  to  effect  this  will  depend  upon 
the  inductance  of  the  coils,  and  also  on  the  strength  of  the 
current  in  the  armature. 

207.  The   lead    of  the  brushes,    besides  tending  to   reduce 
sparking  at  the  commutator,  tends  to  diminish  the  E.  M.  F. 
generated  by  the  armature,   for  two  distinct  reasons  :    First, 
because  it  connects  in  series  armature  windings  in  which  the 
E.  M.  Fs.  are  in  opposition,  as  will  be  seen  from  an  examina- 
tion of  Fig.    156;  and  second,  because  the  M.    M.   F.   of  the 
armature  coils  over  which  the   lead    has    extended    exerts  a 
C.   M.    M.  F.  in  the  main  magnetic  circuit  of  the  field  coils, 
thereby  tending  to  reduce  the  useful  flux  passing  through  the 
armature.      This  effect  is  called  the  back-magnetization  of  the 
armature.       Cross-magnetization,    therefore,    exists   in    every 
armature  as  soon   as  it  generates  a  current,   but  back-mag- 
netization only  exists  when  a  current  is  generated  in  the  arma- 
ture,  and  the  diameter  of  commutation  is  shifted  from  the 
neutral  points. 

208.  The  conditions  which  favor   marked  sparking  at   the 
commutator  of  a  generator  are,  therefore,  as  follows;  namely, 

(i.)  A  powerful  current  in  the  armature;  /.  ^.,  the  sparking 
increases  with  the  load. 

(2.)  A  large  number  of  turns  in  each  coil  connected  to  the 
commutator;  i.  e.,  the  sparking  increases  with  the  inductance. 

(3.)  A  great  distortion  of  the  neutral  line  through  the 
armature,  or  a  powerful  armature  reaction. 

(4.)  A  high  speed  of  rotation  of  the  armature,  since  the 
current  in  the  coil  has  less  time  in  which  to  be  reversed  during 
the  period  of  short  circuiting. 

(5.)  A  nearly  closed  magnetic  circuit  for  each  coil;  /.  e.,  a 
small  reluctance  in  the  magnetic  circuit  of  each  coil,  whereby 
the  inductance  of  the  coil  is  increased. 


ARMATURE   REACTION.  187 

The  conditions  which  favor  quiet  commutation,  or  the 
absence  of  sparking,  are  as  follows;  namely, 

(i.)  A  small  number  of  turns  in  each  commuted  coil,  or  a 
large  number  of  commutator  bars. 

(2.)  Decrease  of  current  strength  through  the  armature. 

(3.)  A  lead  of  the  brushes. 

(4.)  A  powerful  field,  or  a  high  magnetic  intensity  in  the 
entrefer,  due  to  the  M.  M.  F.  of  the  field  magnets. 

(5.)  A  large  reluctance  in  the  magnetic  circuit  of  each  coil. 

209.  An  inspection  of  Figs.  152-154  will  render  it  evident 
that  the  effect  of  superposition  of   the   armature  M.    M.    F. 
upon  the    M.   M.   F.   of  the  field   magnets,  is  to  weaken    the 
intensity  of  the  field  flux  at  the  leading  edges  of  the  pole- 
pieces,  and  to  strengthen  the  intensity  at  the  following  edges  of 
the  pole-pieces.     At  the  same  time,  it  is  necessary  to  advance 
the  brushes;  /.  e.,  the  diameter  of  commutation,  so  as  to  bring 
the  commuted  coils  under  the- leading  edges  of  the  pole-pieces, 
in  order  that  they  may  receive  a  sufficiently  powerful  intensity 
of  field  flux  to  enable  the  armature  current  to  be  reversed  in 
the  coil  under  the  brushes,  and  sparkless  commutation  thus 
to  be  effected.     If,  however,  the  number  of  ampere-turns  on 
the  armature;  i.  e.,  its  M.  M.  F.  at  a  given  load,  be  sufficiently 
great,  the  field  flux  at  the  leading  edges  of  the  poles  will  be  so 
far  weakened,  that  the  intensity  left  there  will  be  insufficient 
to  effect   sparkless    commutation,    no   matter    how  great  the 
lead  may  be.     In  other  words,  the  flux  from  the  armature  will 
overpower  the  field  flux,  in  any  position  of  the  brushes.     This 
will  take  place  when  the  M.    M.   F.  due  to   half  the  turns  of 
active  conductor  on   the  armature,  covered  by  the  pole  face, 
is  equal  to  the  drop  of  magnetic  potential    in   the   field  flux 
through  the  entrefer. 

210.  The  magnetic   intensity  under  the  edge  of  the   lead- 
ing  pole-piece  will  be  zero,  when  the  magnetic  difference  of 
potential    between    this    polar    edge   and   the   armature    core, 
immediately  beneath,  is  zero.     The  magnetic  difference  of  po- 
tential across  the  gap  at  this  point  due  to  the  field  flux  alone, 
will  be  the  magnetic  drop  in  the  entrefer,  or  ($>d,  where  (E,  is 
the  field  intensity  in  the  gap  with  no  current  in  the  armature, 


188  ELECTRO-DYNAMIC  MACHINERY, 

and  d,  the  length  of  the  entrefer  in  cms.     The  total  M.  M.  F. 

of  the  armature,  along  the  arc  of   one  pole,  will   be   --  wp, 

where  wp  is  the  number  of  turns  covered  by  the  pole,  and  this 
will  be  the  total  difference  of  potential  in  the  magnetic  circuit 
of  the  armature.  Assuming  that  the  armature  is  not  operated 
near  the  intensity  of  magnetic  saturation,  almost  the  entire 
reluctance  in  the  armature  circuit  will  be  in  the  entrefer. 
Fig.  156  represents  diagrammatically  the  magnetic  circuit  of 
a  Gramme-ring  armature.  The  reluctance  between  be  and  cd, 
in  the  field  pole,  also  between  ef  and  fa,  in  the  armature,  will 
be  comparatively  small,  so  that  the  total  magnetic  difference 
of  potential  developed  by  the  armature  will  be  expended  in  the 
two  air-gaps  ab  and  de,  half  the  M.  M.  F.  of  the  turns  beneath 
the  pole  face  being  expended  in  each  air-gap.  Strictly  speak- 


FIG.    156. — MAGNETIC   CIRCUITS   OF   GRAMME-RING   ARMATURE   DUE   TO    ITS" 
OWN   M.    M.    F. 

ing,  the  magnetic  flux  produced  by  the  armature  will  not  be 
confined  to  the  paths  indicated  by  the  dotted  arrows,  but  will 
pass  across  the  air-gap  at  all  points  not  situated  on  the  neutral 
line  cf.  The  above  principles  may  be  relied  upon,  however, 
to  a  first  approximation. 

211.  In  order,  therefore,  that  a  smooth-core  armature 
should  be  capable  of  sparkless  commutation,  the  M.  M.  F. 
of  the  turns  on  its  surface,  covered  by  each  pole,  should  be 
somewhat  less  than  the  drop  of  magnetic  potential  in  each 
air-gap,  so  as  to  leave  a  residual  flux  from  the  field  in  which  to 
reverse  the  armature  current  in  the  coil  under  commutation. 
For  example,  if  each  air-gap  or  entrefer  has  a  length  of  2 
cms.,  and  the  intensity  in  the  air  is  3,000  gausses,  the  drop  of 
potential  in  the  air  will  be  6,000  gilberts.  If  the  number  of 


ARMATURE   REACTION.  189 

Gramme-ring  armature  turns,  covered  by  one  pole-piece,  is 
200,  then  a  current  of  80  amperes  from  the  armature  will  repre- 
sent 40  amperes  on  each  side,  and  the  M.  M.  F.,  produced  by 

this  current  will  be  -  -  x  40    X    200   =   10,056    gilberts,  and 

half  of  this  amount,  or  5,028,  being  less  than  the  drop  of  field 
flux  in  the  gap,  should  leave  a  margin  for  sparkless  commu- 
tation. 

212.  Although  the  preceding  rule  enables  the  limit  of  current 
for  sparkless  commutation,  on  a  smooth-core  armature,  to  be 
predicted  under  the  conditions  described,  yet  it  by  no  means 
follows    that    sparkless    commutation    must    necessarily    be 
obtained  if  the  M.  M.  F.  of  the  armature  lies  within  this  limit. 
If,  for  example,  the  number  of  commutator  segments  is  very 
small,  the  inductance  of  each  segment  may  be  considerable, 
and  a  powerful  flux  intensity  may  be  required  to  reverse  the 
current  under  the  brush  in  the  presence  of  such  inductance. 
No  exact  rules  have  yet  been  formulated  for  the  determina- 
tion of  the  inductance  in  a  coil  with  which  a  given  current 
strength,   speed  of  rotation,  and  field  intensity,   shall  render 
sparkless  commutation  possible. 

213.  The  methods   in   general    use  for   the  suppression  of 
sparking  may  be  classified  as  follows: 

(i.)  Those  which  aim  at  the  reduction  of  inductance  in  the 
commuted  coils. 

(2. )  Those  which  aim  at  the  reduction  of  the  current  strength 
passing  through  the  coil  during  its  short  circuit  by  the  brush, 
and,  therefore,  at  the  reduction  of  the  current  strength  which 
must  be  reversed  before  the  short  circuit  is  over. 

(3.)  Those  which  aim  at  the  reduction  of  the  armature  reac- 
tion, so  as  to  reduce  its  influence  in  weakening  the  field  in- 
tensity in  which  the  coil  is  commuted. 

214.  There  are  two  methods  for  reducing  the  inductance  of 
the  armature  coils. 

The  first  is  to  employ  a  great  number  of  commutator  seg- 
ments, thus  decreasing  the  number  of  turns  in  each  coil  under 
commutation.  It  is  evident  that  an  indefinitely  great  number 


*9°  ELECTRO-DYNAMIC  MACHINERY. 

of  commutator  segments  would  absolutely  prevent  sparking. 
A  great  number  of  commutator  segments 'is,  however,  both 
troublesome  and  expensive,  so  that  in  practice  a  reasonable 
maximum  cannot  be  exceeded. 

The  second  method  for  lessening  the  inductance  of  the  arma- 
ture coils  differs  from  the  preceding  only  in  the  method  of 
connection.  It  consists  in  providing  two  separate  windings- 
or  sets  of  coils  ;  or,  as  it  is  sometimes  called,  in  double -winding 
the  armature.  The  two  separate  windings  are  insulated  from 
each  other,  but  are  connected  to  the  commutator  at  alternate 
segments,  so  that  the  brush  rests  coincidently  upon  segments- 
that  are  connected  with  each  winding.  Each  winding  there- 
fore, furnishes  half  the  current  strength,  and  the  effect  of  the 
inductance  in  each  coil  is  reduced. 

215.  When  the  brushes  are  not  so  shifted  as  to  bring  the 
diameter  of  commutation  into  coincidence  with,  or  even  in  ad- 
vance of,  the  neutral  point,  the  coil  under  commutation  will  be 
situated  in  a  magnetic  flux  in  the  wrong  direction;  /'.  <?.,  a  mag- 
netic flux  which  tends  to  increase  and  not  to  reverse  the  cur- 
rent strength  in  the  coil,  so  that  when  the  coil  is  short  circuited 
by  the  brush,  the  current  strength  becomes  increased  in  the 
wrong  direction.  When,  for  any  reason,  it  is  impossible  to 
alter  the  lead  of  the  brushes  during  variations  of  load,  as,  for 
example,  when  the  generator  has  to  run  without  attendance, 
the  sparking,  which  may  be  produced  at  the  brushes  owing  to 
the  resultant  flux  in  which  the  commuted  coils  lie,  may  be 
greater  than  that  due  to  the  mere  reversal  of  armature  current 
in  the  coil  under  the  influence  of  its  inductance.  In  such 
cases,  considerable  improvement  is  effected  by  the  insertion 
of  a  resistance  between  the  coils  and  the  commutator  segments 
with  which  they  are  connected.  Thus  in  Fig.  157,  the  con- 
necting wires  0,2  and  <ri,  are  sometimes  made  of  German  silver. 
It  is  evident,  under  these  circumstances,  that  the  coil  under- 
going commutation  will  not  only  have  its  .own  resistance,  but 
also  the  resistance  of  the  German  silver  wires  in  the  local  cir- 
cuit through  the  brush,  and  the  current  which  can  be  set  up 
in  this  circuit  by  the  E.  M.  F.  induced  in  the  coil,  owing  to 
its  motion  through  the  distorted  field,  is  prevented  from  assum- 
ing considerable  strength.  The  value  of  the  German  silver 


ARMATURE  REACTIONS.  1 91 

resistances,  although  great  by  comparison  with  the  resistance 
of  a  single  coil,  is  small  when  compared  with  the  resistance  of 
the  entire  armature,  and,  consequently,  does  not  greatly  add 
to  the  armature's  effective  resistance.  It  is  clear  that  this 
method  does  not  obviate  the  sparking  due  to  the  inductance 
of  the  armature  coils,  but  tends  rather  to  obviate  that  due  to 
the  establishment  of  unduly  powerful  currents  in  the  short  cir- 
cuited-coil  in  the  wrong  direction,  and  which  current  has  sud- 
denly to  be  reversed  when  the  short  circuit  is  broken.  The 
method  is,  therefore,  often  employed  with  armatures  for  which 
the  brushes  cannot  be  shifted. 

2l6.  The  most  generally  adopted  plan  for  reducing  sparking 
is   to   employ  a  comparatively    high  resistance  in  the  brush 


FIG.    157. — CURRENT   FLOW    IN    ARMATURE   COIL   UNDER   COMMUTATION. 

itself.  An  examination  of  Fig.  157,  will  show  that  if  the  resist- 
ance in  the  tip  of  the  brush  B,  can  be  made  sufficiently  great, 
the  current  which  enters  the  commutator  from  the  wires  will 
be  so  far  reduced,  before  contact  with  the  brush  tip  ceases, 
that  when  the  rupture  does  take  place,  practically  all  the  cur- 
rent from  the  armature  will  be  passing  through  the  coil  in  the 
right  direction;  /.  ^.,  in  the  same  direction  as  it  will  have  when 
the  brush  has  passed  to  the  next  coil,  and,  consequently, 
the  current  strength  which  has  suddenly  to  be  reversed  when 
the  brush  leaves  the  bar  is  very  small. 

217.  Thus  in  Fig.  157,  suppose  the  armature  is  rotating  in 
the  direction  of  the  large  curved  arrow,  and  that  the  commutator 
segment  i,  is  about  to  move  from  beneath  the  brush  B.  The 
coil  2  a  b  c  i,  is  about  to  change  position,  from  the  left-hand  to 
the  right-hand  side  of  the  armature,  and  the  current  in  the  coil 


1 92  ELECTRO-DYNAMIC  MACHINERY. 

is  about  to  change  in  direction,  as  indicated  by  the  small  curved 
arrows,  from  the  direction  a  b  c,  to  the  direction  c  b  a.  The 
current  leaving  the  armature  having  recently  been  flowing  to 
the  brush  B,  from  section  i,  and  the  wire  c  i,  is  now  flowing 
from  sections  2  and  i,  and  from  wires  a  2  and  c  i.  If  the  resist- 
ance in  the  tip  of  the  brush  is  considerable,  relatively  to  that 
in  the  whole  breadth  of  the  brush,  the  current  through  c  i  B, 
will  be  relatively  reduced  and  that  through  a  2  B,  relatively 
increased.  This  will  require,  however,  that  the  current  from 
the  right-hand  side  of  the  armature  shall  be  forced  through 
the  coil  b,  in  the  direction  c  b  ay  and  the  more  nearly  this  can 
be  accomplished,  before  contact  is  broken  between  i  and  B, 
the  less  is  the  opportunity  that  is  offered  for  the  inductance  of 
the  coil  a  b  c,  to  produce  a  spark  at  rupture.  With  this  pur- 


FIG.  158. — DYNAMO    BRUSH    OF   STRIPS   OF   INTERLEAVED    COPPER    AND 
HIGH    RESISTIVITY    METAL. 

pose  in  view,  brushes  are  made  up  of  strips  of  German  silver, 
interleaved  with  copper  or  woven  gauze;  or  they  may  be  made 
of  carbon  with  a  specially  high  resistivity.  Fig.  158  repre- 
sents a  form  of  brush  in  which  strips  of  copper  are  interleaved 
between  strips  of  high  resistivity  metal.  By  this  means  the 
brush,  as  a  whole,  possesses  the  requisite  conductance  for  the 
current  it  has  to  carry,  but  the  tip  has  sufficient  resistance  to 
assist  in  the  reversal  of  the  current  in  the  coil  under  commuta- 
tion. Fig.  159  represents  a  block  of  carbon  employed  in  a 
suitable  holder  or  frame  as  a  dynamo  brush.  In  order  to 
increase  the  conductance  of  the  brush  as  a  whole,  it  is  usually 
thinly  copper-plated  as  shown.  Carbon  brushes  are  largely 
employed  for  i2o-volt  dynamos  where  the  current  strength 
produced  is  not  great,  and  almost  exclusively  employed  with 
5oo-volt  dynamos.  The  use  of  such  brushes  tends  to  reverse 
the  current  in  the  armature,  during  the  period  of  short  circuit- 
ing, and  also  aids  in  checking  any  undue  current  in  the  wrong 


ARMATURE  REACTION.  193 

direction,  caused  by  distortion  of  the  field  flux,  owing  to  arma- 
ture reaction. 

Artifically  compressed  graphite  is  sometimes  used  for  dynamo 
brushes.  Besides  the  advantage  of  high  resistivity,  it  lubricates 
the  commutator  surface. 

2l8.  Referring  now  to  the  tnird  method  for  suppressing 
sparking  at  the  commutator,  a  variety  of  plans  have  been 
attempted  at  different  times  for  bringing  about  a  reversal  of 
the  current  in  a  commuted  coil,  during  the  period  of  short 
circuiting,  by  the  action  of  a  specially  directed  magnetic  flux 
upon  this  coil,  as,  for  example,  by  winding  a  special  magnet 


FIG.  159. — CARBON  DYNAMO  BRUSH. 

placed  with  its  pole  immediately  over  the  short-circuited  coil, 
in  such  a  manner  that  the  flux  from  this  magnet,  penetrating 
the  moving  coil  under  commutation,  may  induce  in  it  an 
E.  M.  F.  sufficiently  powerful,  to  set  up  in  the  short  circuit,  a 
current  strength  equal  to  that  which  the  coil  must  sustain  after 
commutation  is  over,  or,  in  other  words,  to  produce  automati- 
cally the  same  effect  which  the  lead  of  the  brushes  would  be 
capable  of  effecting  under  the  most  favorable  conditions. 
When,  however,  the  current  through  the  armature  and  its 
M.  M.  F.  are  powerful,  the  M.  M.  F.  needed  on  such  control- 
ling magnets  may  require  to  be  very  considerable,  and,  for 
this  reason,  the  plan,  in  this  form,  has  never  come  into  general 
use. 


194 


ELECTRO-D  YNAMIC  MA  CHINER  V. 


219.  In  the  same  direction  a  methocj  has  recently  been  pro- 
posed for  obtaining  sparkless  commutation  by  introducing  into 
the  magnetic  circuit  of  the  machine,  a  M.  M.  F.  equal  in 
amount,  but  opposite  in  direction,  to  that  of  the  armature. 
This  has  the'  effect  of  practically  preventing  all  armature  reac- 
tion and  distortion  of  the  field  flux.  It  is  carried  out  by  wind- 
ing around  the  armature  and  through  the  field  poles,  as  shown 
in  Fig.  160,  a  number  of  turns,  between  A  and  B,  equal  to  that 
of  the  armature  winding,  and  in  series  with  the  armature,  so 
that  the  ampere-turns  in  the  balancing  coil  A  £,  are  equal  and 
opposed  to  the  ampere-turns  on  the  armature.  The  two 
M.  M.  Fs.  thus  counterbalance  and  neutralize  each  other, 
leaving  the  field  flux  practically  unchanged  at  all  loads  of  the 


FIG.   I60. — DEVICE    FOR    PREVENTING    ARMATURE    REACTION. 


machine.  By  this  means  all  sparking  due  to  distortion  of  the 
field  is  prevented,  and  only  the  sparking  due  to  the  inductance 
of  the  commuted  coil,  and  the  current  reversal  in  the  same,  is 
left.  In  order  to  check  this,  an  additional  winding  or  magnet 
over  the  commuted  coil  is  introduced  for  the  purpose  of  revers- 
ing the  E.  M.  F.  in  this  coil  as  above  described,  a  process  which 
is  more  easy  of  application  when  no  armature  reaction  exists 
than  when  armature  reaction  is  unchecked.  A  quadripolar 
machine,  wound  in  this  manner  with  a  quadruple  set  of  balanc- 
ing coils,  is  shown  in  Fig.  161. 

22O.  While  it  is  claimed  for  this  method  that  it  entirely  over- 
comes armature  reaction,  yet  it  possesses  the  disadvantage 
that  it  requires  the  use  of  what  is  practically  an  extra  armature 
winding  upon  a  part  of  the  machine  which  does  not  revolve, 


ARMATURE  REACTION.  195 

thus  introducing  an  additional  cost  and  complexity.  It,  there- 
fore, remains  to  be  determined  how  far  the  advantage  of 
sparkless  operation  is  offset  by  extra  resistance,  weight, 
material,  and  cost. 

Another  method,  which  has  been  tried,  in  England  for  the 
purpose  of  suppressing  sparking,  adds  extra  coils  on  the 
armature,  one  between  each  commutator  segment  and  its 


FIG.    l6l. — QUADRIPOLAR   GENERATOR   WITH    BALANCING   COILS. 


armature  connection.  These  coils  are  arranged  in  such  a 
manner  that  the  E.  M.  F.  induced  in  them  by  their  revolution 
through  the  field  shall  reverse  the  direction  of  the  current  in 
the  coil  under  commutation.  Fig.  162  represents  diagram- 
matically  the  method  of  winding,  and  Fig.  163  the  action  of 
the  various  E.  M.  Fs.  In  Fig.  162  the  inner  ring  with  the 
additional  coils  actually  forms  part  of  the  armature  core  and 
receives  the  flux  from  the  field  although  indicated  in  the  figure 
as  a  separate  ring  for  clearness  of  description.  Fig.  163  shows 
a  coil  being  short  circuited  by  the  brush,  and  the  direction  of 
the  current  in  this  coil  is  being  reversed  by  the  action  of  its 


ig6 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


auxiliary  coil  which  is  still  under  the  trailing  pole  edge,  so 
that  when  the  bar  B,  leaves  the  brush,  no  serious  spark  shall 
follow. 

221.  In  the  dynamo-electric  machine  represented  in  Fig.  6, 
and  which  has  but  three  commutator  segments,  the  spark  is 


FIG.    162. — DIAGRAM    OF    CONNECTIONS   OF   EXTRA   ARMATURE    COILS    FOR 
CHECKING    SPARKING. 

prevented  from  forming  by  an  air  blast  directed  against  the 
commutator  in  such  a  manner  as  to  extinguish  the  incipient 
spark  at  the  breaking  of  the  short  circuit.  This  air  blast  is 


FIG.    163. — DIAGRAM   INDICATING   ACTION   OF   DEVICE   ILLUSTRATED   IN 

FIG.    156. 

supplied   by   a   small    centrifugal    pump    rotating    with   the 
armature. 


222.  The  number  of  bars  in  the  commutator  of  a  generator 
depends  principally  upon  the  sparking  limit.  If  there  were  no 
danger  of  excessive  sparking,  the  number  of  commutator  bars 
in  any  machine  would  be  very  small,  except  when  marked 
freedom  from  pulsation  is  required  in  the  current  strength. 


ARMATURE   REACTION.  197 

The  number  of  bars  will,  therefore,  depend  upon  the  pressure 
and  current  strength,  the  armature  reaction,  and  the  field  flux 
intensity.  An  unduly  small  number  of  bars  leads  to  excessive 
sparking,  and,  in  the  case  of  high  pressure  machines,  the 
sparks  may  flash  completely  around  the  commutator,  produc- 
ing what  is  practically  a  short  circuit.  Small  machines  have 
been  built,  however,  giving  10,000  volts  with  only  32  commuta- 
tor segments. 

223.  Thus  far  we  have  mainly  considered  smooth-core 
armatures.  The  great  majority  of  dynamos,  in  construction 
at  the  present  time  are,  however,  toothed-core  armatures.  In 
the  first  production  of  toothed-core  machines,  the  sparking 
which  they  exhibited  was  more  troublesome  and  violent  than 
in  smooth-core  armatures  of  equal  size,  and  apparently  for 
the  reason  that  the  inductance  of  each  armature  coil  was 
increased,  owing  to  its  being  surrounded,  or  nearly  surrounded, 
by  iron,  instead  of  having  an  iron  base  only,  as  in  the  smooth- 
core  type.  This  difficulty  has  since  been  overcome  by  care- 
ful designing,  and  toothed-core  armatures  are  now  con- 
structed which  give  less  trouble  from  sparking  than  smooth- 
core  armatures  of  equal  size  and  output.  This  is  accomplished 
by  giving  such  a  cross-section  to  the  teeth  in  the  armature 
that,  at  no  load,  the  iron  in  the  teeth  is  nearly  saturated,  and 
has,  therefore,  a  high  reluctivity.  The  presence  of  armature 
reaction  tends  to  increase  the  magnetic  intensity  in  the  teeth 
beneath  the  trailing  pole  edges,  and  to  diminish  it  in  the  teeth 
beneath  the  leading  pole  edges,  as  already  observed.  This 
tendency  is  opposed  by  the  increasing  reluctivity  of  the 
saturated  teeth  at  the  trailing  pole  edges,  and,  consequently, 
the  teeth  tend  to  restore  an  equal  distribution  of  magnetic  flux 
over  the  surface  of  the  armature;  or,  in  other  words,  tend  to 
check  the  effect  of  armature  reaction.  At  the  same  time,  the 
high  reluctivity  of  the  teeth  tends  to  diminish  the  inductance 
of  each  coil  undergoing  commutation,  so  that,  by  careful 
adjustment,  the  existence  of  the  teeth  is  not  merely  a  mechan- 
ical advantage  but  also  a  considerable  electrical  advantage. 

In  practice,  the  output  of  a  generator  is  not  really  limited 
by  excessive  sparking.  As  usually  designed,  the  temperature 
elevation  of  the  armature,  even  when  thoroughly  ventilated, 


I98  ELECTRO-DYNAMIC  MACHINERY. 

fixes  the  limit  to  the  output  before  the  sparking  becomes  trou- 
blesome. And,  in  fact,  many  generators  are  in  use  to-day 
which  never  require  to  have  any  lead  given  to  their  brushes, 
and  need  only  occasional  attention  to  their  commutators. 

224.  In  the  preceding  discussion,  we  have  considered 
armature  reaction  from  the  standpoint  of  the  Gramme-ring 
armature  only,  but  the  same  principles  are  equally  applicable 
to  disc  or  drum  armatures.  » 


CHAPTER  XIX. 

HEATING    OF    DYNAMOS. 

225.  The   activity   expended   in    any   generator   invariably 
takes  the  form  of  heat.     These  expenditures  are: 

(i.)  7a  R  activity  in  the  field  magnets. 

(2.)  /3  R  activity  in  the  armature  winding. 

(3.)  72  R  activity  in  eddy  currents,  in  armature  and  field. 

(4.)  Hysteretic  losses  in  armature  core  and  field  poles. 

(5.)  Friction  in  bearings  and  brushes. 

(6. )  Friction  in  air. 

226.  The  number  of  watts  expended   in  the  field  magnets 
is  equal  to  the  product  of  the  pressure  in  volts  at  the  field 
terminals,    multiplied    by    the    current    in    amperes    passing 
through  the  field.     This  activity,  although  steadily  expended 
in    the   form    of   heat,   is    necessary    in  order  to  produce  the 
M.  M.  F.  of  the  field-coils.     In  a  certain   sense,  therefore,  it 
may  be  said  that  the  /2  R  activity  in   the  field  windings  is 
expended  in  order  to  magnetize  the  field,  and  the  73  R  activity 
in  the  armature  winding  is  expended  in  order  to  magnetize  the 
armature.     In  series-wound  generators,   where  the  armature 
sends    its    entire    current    through    the    field    magnets,    this 
expenditure  varies  with  the  load.     Thus,  in  a  ro-KW  series- 
wound  generator,  designed  to  supply  a  maximum  current  of 
200  amperes  at  50  volts  pressure,  if  the  resistance  of  the  field 
magnet  coils,  when  warm,  be  o.oi   ohm,  the  pressure  at  the 
terminals  of  the  magnets  will  be  200  x  o.oi  —  2  volts,  and 
the  activity,  2  x  200  =  400  watts.     On  light  load,   however, 
of  say  20  amperes,  the  pressure  will  be  o.oi  x  20  =  0.2  volt, 
and  the  activity  o.  2  x  20=4  watts,  so  that,  in  the  first  case, 
the  amount  of  heat  generated  in  the  field  winding  is  100  times 
greater  than  in  the  second  case,  and  the  temperature,  which 
the  field  winding  would  attain  in  the  first  case,  would  be  much 
higher  than  in  the  second. 


200  ELECTRO-DYNAMIC  MACHINERY. 

227.  In  a  shunt-wound   generator,  the  activity  in  the  field 
circuit  is  nearly  constant.     For  example,  a  lo-KW  generator, 
intended  to  supply  in  volts  at  its  terminals,  at  full  load,  with 
a  current  strength  of  90  amperes  in  the   main   circuit,  might 
supply  a  current  of   2.5  amperes  through  its  field  magnets. 
Consequently,  the  activity  in   the   field-magnet  circuit  would 
be    in    x    2.5   —   277.5    watts.     At    light   load,    the  current 
strength  through  the  field  magnets  would  have  to  be  reduced 
to  say  2.0  amperes,  in  order  to  keep  the  terminal  pressure  at 
in   volts,  and  the  activity  in  the  field  would  be  reduced  to- 
in  x  2.0  —  222  watts,  so  that  the  temperature  attained  by  the 
winding  on  the  field   magnets  would  not  be  much  greater  at 
full  load  than  at  no  load. 

228.  It  is  evident  that  the  /2  R  activity  in  the  armature 
always  varies  with  the  load;    /'.  <?.,  with  the  current  strength 
/.     At  no   load,  this   loss    must   be   very  small,    the    current 
strength  being  limited  to  that  required  for  the  excitation  of  the 
field  magnets.     The  temperature  elevation  of  the  armature, 
due  to  the  armature  winding,  consequently,  increases  rapidly 
with  the  load. 

229.  The  activity  expended  as  7s  R,  in  eddy  currents  in  the 
field  poles,  or  in  the  armature,  is  nearly  uniform  at  all  loads, 
especially  in  shunt-wound  machines,  in  which  the  intensity  of 
magnetic  flux  is  nearly  constant,  and  if  this  intensity   were 
absolutely  uniform;  /'.  <?.,  if  there  were  no  drop  in  the  armature, 
requiring  a  greater  M.  M.  F.  and  exciting  current,  and  if  there 
were   no  armature  reaction,  the  eddy  current  loss  would  be 
constant  at  all  loads. 

230.  The  activity  expended  in  hysteresis  in  the  armature  and 
field  poles,  would,  similarly,  be   constant   at  all   loads   if  the 
magnetic  intensity  were  constant.     As  the  magnetic  intensity 
is   increased   by  an  increase    in  the  M.    M.    F.   of  field   and 
armature  at  full  load,  the  hysteretic  loss  increases,  approxi- 
mately following  the  i.6th  power  of  the  local  magnetic  intensity 
at  any  point.     The  heat  due  to  hysteretic  loss  is  developed 
principally  in  the  armature. 


HEATING   OF  DYNAMOS.  201 

231.  The  friction  in  bearings  and  brushes  produces  heat  at 
those    parts.     The   amount   of    heat   liberated,    due   to    pure 
friction,    is  comparatively  small  when  the  lubrication    of  the 
bearings  is    properly  attended    to.     In    large  genefators,   the 
heat   produced    by    the   friction    of  the  brushes  on  the  com- 
mutator is  very  small  compared  with  the  heat  developed  by 
the   sparking,  and  the   powerful  currents  set  up  in  the  short 
circuited  coils  undergoing  commutation. 

The  frictional  forces  opposing  the  rotation  of  an  armature 
in  which  there  is  no  appreciable  magnetic  flux,  are  due  to 
gravitation;  /'.  e.,  to  the  weight  of  the  revolving  parts.  When, 
however,  the  field  magnets  are  excited,  and  magnetic  flux 
passes  through  the  armature,  the  frictional  forces  are  due  to 
gravitation  and  magnetic  attraction  combined.  If  the  arma- 
ture is  situated  symmetrically  with  respect  to  an  external 
system  of  field  magnets,  if  for  example,  the  Gramme-ring 
armature  of  Fig.  129  be  revolved  concentrically  with  the  polar 
bore,  the  system  of  magnetic  forces  all  round  the  machine  will 
balance,  and  the  friction  of  the  machine  will  not  be  increased 
by  the  influence  of  the  magnetic  flux.  If,  however,  the 
armature  were  nearer  the  lower  poles,  so  that  the  entrefer 
was  shorter  beneath  the  armature  than  above  it,  there  would 
be  a  tendency,  as  we  have  seen,  to  produce  a  greater  magnetic 
intensity  in  the  lower  magnetic  circuits  than  in  the  upper  ones, 
with  a  corresponding  resultant  magnetic  pull  upon  the  arma- 
ture, vertically  downward.  The  armature  would  consequently 
revolve  in  its  bearings  as  though  its  weight  were  increased, 
and  with  an  increase  in  friction  and  frictional  expenditure  of 
energy.  On  the  other  hand  if  the  armature  were  centred  too 
high,  so  as  to  develop  greater  magnetic  fluxes  in  the  upper 
than  in  the  lower  magnetic  circuits,  the  effective  weight  of  the 
armatur^  in  its  journals  would  be  reduced,  and  the  frictional 
waste  of  energy  in  them  diminished.  This  principle  has  been 
employed  in  the  design  of  some  bipolar  machines,  in  which  the 
resultant  magnetic  attraction  upon  the  surface  of  the  armature 
is  upwards,  or  in  opposition  to  the  attraction  of  gravitation. 

232.  The  friction  due  to  the  churning  of  the  air  is  compara- 
tively   small    in    drum    armatures,    but    often   constitutes   an 
appreciable  loss  in  alternators,  when  a  Gramme-ring  armature 


202  ELECTRO-DYNAMIC  MACHINERY. 

of  large  diameter  and  rough  exterior  is  revolved  at  a  high 
speed.  In  this  friction  the  heat  is  principally  developed  in 
the  surrounding  air  and  not  in  the  mass  of  the  machine.  The 
air  churning,  on  the  contrary,  assists  in  cooling  the  machine. 

233.  The  magnetic  stresses  exerted  in  large  electro-dynamic 
machines  are  often  of  considerable   amount.      Referring    for 
example  to  the  machine  outlined  in  Fig.  129,  the  polar  areas 
are  1,400  sq.  cms.,  and  the  useful  magnetic  flux  passing  per- 
pendicularly into  the  armature,  3.534  megawebers.     The  mean 

intensity  in  the  entrefer  is  therefore  :     —  =  2, 5  24  gausses. 

B2 

The  attractive  force  per  square  centimetre  (Par.  72)  is--   = 

oTt 

— =  253,400  dynes  =  258.4  grammes.      The   total 

stress  exerted  will  be  1,400  x  258.4  :=  361.700  grammes  = 
797.4  Ibs.  weight,  at  each  pole. 

234.  In  drum  or  Gramme-ring  armatures  with  radial  field 
magnets,  the   magnetic  flux  through  the  armature,   can    only 
alter,  within  certain  limits,  the  vertical  forces  acting  upon  the 
armature  due  to  gravitation.     In  machines  with  parallel  field 
magnets,  as  for  example,  in  the  dynamo  of  Fig.  8,  the  magnetic 
stresses  exerted  upon  the  armature  are  side  thrusts,  or  hori- 
zontal stresses  parallel  to  the  axis  of  the  shaft.     If  the  entrefer 
on  each   side  of  the  armature  has  the   same  length,  the  two 
resultant  magnetic  forces  exerted  upon  the  armature  will  be 
equal,  but  if  the  armature  is  nearer  one  set  of  poles  than  the 
other,  so  as  to  produce  a  shorter  entrefer  on  one  side  than  on 
the  other,  there  will  be  a  tendency  to  produce  a  resultant  side 
thrust  toward  the  side  of  shorter  entrefer.     It  is  important, 
therefore,    that   generators    of    this   type    should    have    their 
armatures  nearly  midway  between  the  polar  faces. 

235.  The  expenditure  of  energy  as  heat  in  a  generator  is 
objectionable,  first,  because  it  represents  loss  of  power,  and, 
consequently,  reduced  efficiency.     Ten  per  cent,  of  loss  in  the 
generator  due  to  all  these  causes  combined,  means  approxi- 
mately 10  per  cent,  more  coal,  10  per  cent,  more  water,  and 


HEATING  OF  DYNAMOS.  203 

engines  and  boilers  larger  by  10  per  cent,  to  supply  a  given  elec- 
tric activity,  than  would  be  necessary  if  it  were  possible  to 
avoid  these  losses  entirely;  and  second,  because  the  heat 
developed  may  raise  the  temperature  of  the  generator  to  an 
objectionably  high  degree  and  ultimately  limit  its  output. 

236.  There  are  four  limitations  to  the  output  of  a  continuous- 
current  generator;  viz., 

(i.)  Insufficient  mechanical  strength  to  withstand  the 
mechanical  forces  brought  into  play. 

(2.)  Insufficient  efficiency,  or  insufficient  electric  pressure 
at  the  brushes,  under  load. 

(3.)  Excessive  sparking. 

(4.)  Excessive  heating. 

The  first  two  cases  of  limitation  can  always,  by  proper 
design,  be  obviated  in  all  but  the  smallest  generators.  It  is 
the  third  and  fourth  considerations  which  limit  the  output  in 
all  practical  cases.  In  modern  machinery  it  is  the  heating 
which  first  limits  the  output. 

237.  The  limiting  temperature  of  the  generator  armature  is 
dependent  upon  a  variety  of  considerations.     In  the  first  place, 
the   hotter   the   armature   winding    becomes,   the   greater   its 
resistance;  for,  if  r,  be  the  resistance  of  the  armature,  in  ohms, 
at   o°  C,  its  resistance  ./?,  at  any  temperature   /°  C.,  will  be 
approximately,  R  =  r  (i  -(-  0.004  *)•     In  other  words,  the  re- 
sistance will  rise  by  0.4  per  cent,   per  degree  centigrade  of 
temperature  elevation  above  zero.     The  result  is,  that  at  high 
temperatures,  the  wasteful  activity,  as  /'^,  in  the  armature, 
increases,  increasing  thereby  both  the  loss  in  the  machine  and 
the  tendency  to  temperature  elevation. 

238.  The  temperature  of  the  armature  must  not  exceed  that 
at  which   any  of  the    materials  employed  in   its  construction 
would  be  deleteriously  affected;  *.  e.,  either  softened  or  decom- 
posed.    In  many  generator  armatures,  cotton  is  the  insulator 
employed,  four  thicknesses  of  cotton  (representing  each  about 

th  of  an  inch,  separates  adjacent  wires,  except  at  specially 

130 

protected   places,   where   mica   and    oil  paper  are   employed. 


204  ELECTRO-DYNAMIC  MACHINERY. 

Cotton  undergoes  slow  thermolysis,  or  decomposition  by  heat, 
at  a  temperature,  approximately,  that  of  the  boiling  point  of 
water,  or  100°  C.  Consequently,  it  is  unsafe,  in  practice,  to 
maintain  cotton  covered  armatures,  even  though  shellac-var- 
nished, at  a  higher  temperature  than  100°  C.  If  the  tempera- 
ture of  the  room,  in  which  a  generator  is  operated,  never 
exceeded  30°  C.,  it  would  require  an  elevation  of  70°  C.  in 
the  armature  to  reach  a  dangerously  high  temperature.  As, 
however,  some  engine  rooms  attain,  in  summer,  a  higher 
temperature  than  30°  C.,  and  since  a  margin  has  to  be  left  for 
accidental  overloads,  50°  C.  is  the  temperature  elevation  that 
the  armature  should  not  exceed  at  full  load,  and  modern  practice 
is  reducing  this  to  40°  C. ;  so  that  the  temperature  of  the 
armature,  as  observed  after  several  hours  of  full  load,  is  usually 
specified  not  to  exceed  40  Q  C.  of  temperature  elevation  above 
the  surrounding  air. 

United  States  Navy  specifications  usually  require  that  the 
elevation  of  temperature  shall  not  exceed  50°  F.  =  27.8°  C., 
at  any  part  of  the  machine.  Other  things  being  equal,  these 
specifications  can  only  be  met  by  increasing  the  size  of  machine 
for  a  given  output.  In  other  words,  with  machines  of  the  same 
grade,  a  reduction  of  the  limiting  temperature  at  full  load 
means  a  reduction  of  the  load  which  the  machine  can  carry. 

239.  Many  large  generators,  however,  do  not  use  any  insul- 
ation for  their  armature  conductors,    except  mica,   and   such 
•generators  can  safely  carry  a  much  higher  temperature  eleva- 
tion without  danger. 

Here  the  dangerous  temperature,  so  far  as  mechanical  injury 
of  the  armature  is  concerned,  would  be  that  at  which  solder 
would  melt.  Electrically,  however,  the  increase  in  the  resist- 
ance in  the  armature  would,  probably,  constitute  a  limitation 
long  before  this  temperature  was  reached,  and  if,  in  fact,  the 
armature  winding  were  to  attain  this  temperature,  the  field 
coils,  and  even  the  bearings  of  the  machine,  might  be  danger- 
ously overheated. 

-  .  •  i 

240.  The  activity  in  the  field  coils,  which  will  elevate  their 
external  temperature  a  given  number  of  degrees  centigrade, 
depends  upon  their  shape,  size  and  arrangement,  whether  their 


HEATING   OF  DYNAMOS.  205 

surfaces  are  freely  exposed  to  the  air,  or  are  partly  sheltered 
from  it.  Usually,  however,  the  surfaces  of  the  field  coils  must 
afford  16  square  centimetres,  or  about  2.5  square  inches  per 
watt  of  activity  developed  in  them  as  I*  R  heat.  If  the  field 
winding  consists  of  many  layers  of  fine  wire,  the  temperature  of 
the  deep  seated  layers  will  be  greater  than  that  of  the  super- 
ficial layer  ;  but  if,  on  the  contrary,  the  layers  be  few,  and  the 
wire  coarse,  the  difference  of  temperature  in  the  winding  will 
be  inconsiderable.  The  elevation  of  temperature  on  the  field 
magnets  of  a  generator  is  usually  not  greater  than  30*  C.  at 
full  load. 

241.  In  the  case  of  the  armature,  the  speed  at  which  it 
revolves  through  the  air  greatly  increases  its  capability  for 
•dissipating  heat  and  reducing  its  temperature,  so  that  a  much 
greater  surface  thermal  activity  can  be  permitted  in  the  arma- 
ture than  in  the  field  coils.  The  usual  allowance  for  eddy  cur- 
rents, load  currents  and  hysteretic  losses  combined,  is  about 

—  th  watt  per  square  centimetre;  i.  e.y  i—  watts  per   square 

0  *5 

inch  of  armature  surface,  including  the  surface  on  the  sides  of 
the  armature,  but  excluding  its  internal  core  surface  ;  or,  about 
three  times  more  activity  per  unit  area  than  on  the  field  mag- 
nets. In  some  specially  ventilated  armatures,  in  which  the 
core  discs  are  spaced  and  separated  at  intervals,  to  permit  the 
circulation  of  air  from  the  interior  outward  by  centrifugal  force, 
the  dissipation  of  heat  can  be  so  far  increased  that  two  watts 
per  square  inch  of  armature  surface  have  been  rendered  practic- 
able. Much  depends,  however,  upon  the  shape  and  size  of 
the  armature,  as  well  as  upon  its  peripheral  speed,  so  that  no 
exact  rule  can  be  laid  down. 


CHAPTER  XX. 

REGULATION    OF    DYNAMOS. 

242.  As  has  already  been  pointed  out  (Par.  16),  all  self-excit- 
ing continuous-current  generators  may  be  wound  in  one  of 
three  ways  ;  namely, 

(i.)  Series-wound. 
(2.)  Shunt-wound. 
(3.)  Compound-wound. 

243.  Fig.   164  represents  diagrammatically  the  connections 
between  the  field  and  armature  of  a  series-wound  generator. 


FIG.   164. — DIAGRAM   OF    SERIES    WINDING. 

It  will  be  observed  that  the  current  in  the  main  circuit  passes 
through  the  field  magnet  windings.  The  M.  M.  F.  of  the  field 
coils,  therefore,  increases  directly  with  the  current  strength 
through  the  circuit.  So  long  as  the  iron  in  the  magnetic  cir- 
cuit of  the  machine  is  far  from  being  saturated,  the  flux  through 
the  armature  increases  with  the  M.  M.  F.,  approximately,  in 
direct  proportion,  and  the  E.  M.  F.  of  the  armature,  conse- 
quently, increases  nearly  in  proportion  to  the  current  strength. 
As  soon  as  the  iron  in  the  circuit  approaches  saturation,  the 
flux  increases  more  slowly,  and  finally,  the  E.  M.  F.  of  the 
armature  is  scarcely  increased  by  any  increase  in  the  current 
strength  through  the  circuit. 

244.  Fig.  165  represents  diagrammatically  the  connections, 
between  the  field  and  armature  of  a  shunt-wound  generator. 

206 


REGULATION  OF  DYNAMOS. 


207 


Here  the  field  magnets  are  wound  with  fine  wire  and  the 
windings  are  connected  in  parallel  with  the  external  circuit, 
instead  of  being  connected  in  series  with  it.  Consequently, 
if  the  pressure  at  the  brushes  be  considered  as  uniform,  the 
current  strength  passing  through  the  magnet  coils  must,  by 
Ohm's  law,  be  uniform,  independent  of  the  current  strength 
in  the  main  circuit.  Thus,  if  the  pressure  at  the  brushes  be 
assumed  constant,  at,  say  100  volts,  and  the  resistance  of  the 
magnet  coils  be  50  ohms,  then  the  current  strength  through 
the  magnet  coils  will  be  two  amperes,  independently  of  the 
strength  of  current  supplied  to  the  main  circuit. 

245.  Practically,  however,  owing  to  the  drop  of  pressure  in 
the  armature  as  the  load  increases,  and  also  on  account  of  the 


FIG.    165. — DIAGRAM    OF    SHUNT   WINDING. 

shifting  of  the  brushes  that  may  be  necessary  with  the  increase 
of  load,  the  pressure  at  the  brushes  diminishes,  and  the  cur- 
rent  strength  through  the  field  magnets  diminishes  in  the  same 
proportion.  The  tendency  in  a  shunt-wound  machine  is,  there- 
fore, to  diminish  its  M.  M.  F.,  and  its  resulting  E.  M.  F.,  as  the 
load  on  the  generator  increases.  In  order  to  maintain  a  con- 
stant pressure  at  the  brushes  under  all  variations  of  load,  it  is 
necessary  to  adjust  the  strength  of  current  passing  through 
the  field  magnets,  so  that  the  M.  M.  F.  at  full  load  shall  be 
slightly  in  excess  of  the  M.  M.  F.  at  light  load.  This  is  usually 
accomplished  by  the  insertion  of  a  rheostat  in  the  field  magnet 
circuit,  so  that  some  or  all  of  this  resistance  can  be  cut  out  by 
hand  at  full  load,  thereby  increasing  the  current  strength 
through  the  magnet  coils. 

246.   If,  for  example,  the  full-load   activity  of  the  machine 
be  10  KW  at  100  volts  pressure,  the  full-load  current  strength 


208 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


will  be  ioo  amperes.  Assuming  the  resistance  of  the  armature 
to  be  0.05  ohm,  the  drop  of  pressure  in  the  armature  at  full 
load  will  be  ioo  x  0.05  =5  volts,  and  the  additional  drop  of 
pressure,  owing  to  the  shifting  of  the  brushes  in  order  to 
avoid  sparking,  may  be  2  volts  more,  making  a  total  drop 
in  pressure  of  7  volts.  The  effect  of  this  drop  would  be 
to  reduce  the  current  strength  in  the  field  magnet  coils  from 

2  amperes  to  —  =  1.86  amperes,  thus  reducing  both  the  flux 

0 

through  the  armature  and  the  E.  M.  F.,  so  that  a  balance 
between  the  E.  M.  F.  and  its  excitation  might  be  found  at, 
say,  90  volts,  if  no  means  were  adopted  to  regulate  the  cur- 
rent strength  through  the  field  coils.  In  other  words,  the 


FIG.    l66. — DIAGRAM   OF   COMPOUND    WINDING. 

pressure  at  the  brushes  would  vary  by  10  volts  between  light 
and  full  load. 


247.  Fig.  166  represents  the  connections  between  the  field 
and  armature  of  a  compound-wound  generator.  Here  the 
principal  M.  M.  F.  furnished  by  the  magnet  coils  is  that  due 
to  the  shunt  coil,  composed  of  many  turns  of  fine  wire,  an 
auxiliary  series  coil,  of  comparatively  few  turns  of  coarse  wire, 
being  also  employed  in  the  main  circuit.  As  the  load  increases, 
the  M.  M.  F.  generated  by  the  shunt  winding  tends  to  diminish 
as  above  described,  but  the  M.  M.  F.  due  to  the  series  coil 
increases.  By  suitably  proportioning  these  two  opposite 
influences,  the  M.  M.  F.  may  be  automatically  so  controlled, 
that  the  pressure  at  the  brushes  shall  remain  constant, "either 
at  the  brushes  of  the  generator,  or  at  the  terminals  of  the 
motor  or  other  translating  device,  which  may  be  situated  at  a 
considerable  distance  from  the  generator.  In  order  to  effect 
this  latter  result,  the  M.  M.  F.  of  the  series  coil  must  compen- 


REGULATION  OF  DYNAMOS.  209 

sate  not  only  for  the  drop  in  the  armature,  but  also  for  the 
drop  in  the  conductors  leading  from  the  generator  to  the 
motor,  so  that  these  external  conductors  may  be  regarded, 
electrically,  as  forming  an  extension  of  the  armature  winding, 
and,  in  this  sense,  the  generator  delivers  a  constant  pressure 
at  its  final  terminals  on  the  motor.  Such  a  machine  is  said  to 
be  over  compounded. 

248.  Series-wound  generators  are  almost  invariably  employed 
for  series-arc  lighting,  since  it  would  be  very  difficult  to  supply 
the  required  M.  M.  F.  far  their  magnets  by  a  shunt  winding, 
considering  that  the  pressure  at  the  brushes  varies  between  such 
wide  limits;  and,  even  if  such  shunt  winding  could  be  supplied, 
it  would  necessarily  be  formed  of  a  very  long  and  fine  wire, 
and,  consequently,  would  become  troublesome  and  expensive. 
Series  arc-lighting  generators  are  sometimes  constructed  for 
as  many  as  200  lights,  representing  about  10,000  volts  at  the 
generator  terminals  at  full  load,  and  a  shunt  winding  for  such 
a  pressure  would  be  very  expensive. 

249.  Shunt-wound  generators  are  usually  employed  for  sup- 
plying   incandescent    lighting    from   a   central     station,    and 
their  pressure  is  varied  by  hand  regulation. 

Compound-wound  generators  are  usually  employed  for  sup- 
plying motors  from  central  stations,  and  also  for  incandescent 
lights  and  motors  in  isolated  plants. 

250.  In  the  design  and  use  of  generators,  it  is  important  to 
know  how  the  E.  M.  F.  generated  in  the  armature  at  a  given 
speed  varies  with  the  current  passing  through  the  field  magnets. 
We  have  seen  that  so  long  as  the  brushes  remained  unaltered 
in  position,  the  E.  M.  F.  in  the  armature,  in  C.  G.  S.  units,  is 
equal  to  the  product  of  the  number  of  turns  on  the  armature, 
the  number  of  useful  webers  passing  through  the  armature 
from  each  pole,  and  the  number   of   revolutions  per   second. 
Consequently,  the  E.  M.   F.    of   such    an    armature,   running 
at  a  constant  speed,  depends  .directly   upon  the  flux  through 
its    magnetic    circuit   or    circuits.     If    we  vary    the   current 
strength  through  the  field   magnets,  and,    consequently,  the 
M.  M.  F.,  we  can  observe   the   pressure  in  volts,  which   the 


210 


ELECTRO-DYNAMIC  MACHINERY. 


machine  will  deliver  at  its  brushes  at  light  load.  A  series 
of  such  observations,  plotted  in  a  curve,  gives  what  is  called 
the  characteristic  curve  of  the  generator.  In  the  case  of 
a  self-exciting,  series-wound  generator,  it  is  only  possible  to 


100 


50 


30 


20r 


IO  2O 

AMPERES 


70 


FIG.   167. — CURVE   OF   E.     M.    F.    DEVELOPED    IN   THE    ARMATURE   OF   A   SERIES- 
WOUND  DYNAMO,  WITH  REFERENCE  TO  CURRENT  STRENGTH  IN  A  CIRCUIT. 

vary  the  M.  M.  F.  by  varying  the  load,  and,  consequently,  by 
including,  in  the  pressure  at  the  brushes,  the  drop  taking  place 
in  the  armature.  The  curve  obtained  from  a  series-wound 
machine  under  such  circumstances,  is  called  an  external  char- 
acteristic^ and  the  internal  characteristic  may  be  determined  from 
it  by  correcting  for  the  drop  in  the  armature. 


REGULATION  OF  DYNAMOS.  21  1 

251.  Fig.  167  represents  the  internal  and  external  charac- 
teristics of  a  particular  series-wound  generator  intended  to 
supply  a  maximum  of  70  amperes  at  50  volts  terminal  pressure 
or  3,500  watts. 

The  pressure  at  terminals,  when  the  load  was  varied  so  as  to 
produce  the  required  variations  of  current  strength  through 
the  magnets,  followed  the  broken  line  A  B  C,  which  is,  there- 
fore, the  external  characteristic  of  the  machine.  If  we  add  to 
the  ordinates  of  this  line  from  point  to  point,  the  drop  of  pres- 
sure in  the  armature  at  the  corresponding  current  strength,  the 
full  line  o  D  E  F,  is  obtained,  which  is,  therefore,  the  internal 
characteristic  of  the  generator  or  the  curve  of  its  E.  M.  F.  in 
relation  to  the  exciting  current  in  its  field  coils. 

The  useful  E.  M.  F.  developed  by  the  armature  may  be 
expressed  by  the  formula, 

E  —  -  -  -  -  volts. 

x 


so  that,  if  two  observations  are  secured,  the  whole  internal 
characteristic  curve  may  be  deduced  to  a  very  fair  degree  of 
accuracy.  For  example,  in  Fig.  167,  the  E.'  M.  F.  at  20 
amperes  =  74  volts,  and  at  70  amperes,  95  volts.  From  these 
observations  we  may  take  the  two  equations, 

20  70 

74  =  -  -  and  95  = 


x  -\-  20 y  x  -j- 

From  these  two  equations  we  obtain  x  =  0.0836  and  y  = 
0.00933,  so  that  the  E.  M.  F.  at  any  current  strength  through 
the  field  magnets  is 

E  =  —  7 volts. 

0.0836  -\-  0.00933  / 

The  dotted  curve  o  HE  F,  which  lies  close  to  the  full  curve 
o  D  E  F,  represents  the  locus  of  this  equation.  It  will  be 
observed  that  the  dotted  line  practically  coincides  with  the 
full  line  representing  the  observations,  except  within  the  first 
20  amperes  of  magnetizing  current  strength. 

252.  Fig.  168  represents  the  characteristic  curve  of  a  shunt- 
wound  generator,  of  200  KW  capacity.  Here  the  current 
strength  through  the  field  magnets  was  not  observed,  but  the 
pressure  acting  on  the  field  coils  was  noted.  Assuming,  as 
would  probably  be  very  nearly  true,  that  the  resistance  of  the 


212 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


field  magnet  coils  remained  constant  throughout  the  observa- 
tions, the  exciting  current  strength  would  be  proportional  to 
the  pressure  acting  on  the  coils.  With  40  volts  on  the  magnets, 
the  E.  M.  F.  at  the  brushes  with  the  external  circuit  broken 
was  71  volts,  and  increased,  as  shown  by  the  full  line  A  B  C,  to 


180 
170 

^9 

> 

X 

160 

> 

^ 

/ 

^ 

B, 

f 

130 

/ 

120 

/ 

/ 

j 

* 

90 

/ 

" 

80 

// 

~j 

i 

/ 

si 

/ 

It 

mA/l 

/ 

£ 

/ 

/ 

/ 

P 

7 

0         10       2         30      40       60      J50       70       80       90     .100     UO     120     130     14» 
VO.LTS  ON  FIELD 

FIG.    168.  —  CHARACTERISTIC   CURVE   OF   SHUNT-WOUND   DYNAMO. 

185  volts,   with   140   volts   on   the   magnets.      Here  also  the 
E.    M.   F.,   £,   may   be   expressed   by   the   Frolich    equation, 

E  =  -  :  -  ,  e  being  the  pressure  on  the  field  magnets;  taking 
x  -j-  yc 


the  two  observations,  120  = 


—  — 


and  174  = 


we 


^+    I20/ 

find  x  =  0.43  and  jy  =  0.0022,  from  which  the  general  equation 
becomes,  ^  e 


E  = 


0.43  -j-  0.0022  e 


volts. 


REGULA  TION  OF  D  YNAMOS.  2 1 3 

The  locus  of  this  equation  is  represented  by  the  dotted  line, 
which  practically  coincides  with  the  full  line  A  B  Ct  of 
observation. 

253.  When,  therefore,  two  reliable  observations  have  been 
made  of  the  E.  M.  F.  generated  by  an  armature,  at  observed 
exciting  current  strengths,  or  pressures,  situated  not  too  closely 
together,  it  is  possible  to   construct  the  characteristic  curve 
throughout  to  a  degree  of  accuracy  sufficient  for  all  practical 
purposes. 

The  Frolich  equation,  by  which  this  is  possible,  is  a  con- 
sequence of  the  fact  that  the  reluctance  of  the  air  paths  in  the 
magnetic  circuit  of  a  generator  is.  constant,  while  the  reluc- 
tivity of  the  iron  in  the  circuit  is  everywhere  capable  of 
being  expressed  by  the  formula  v  =  a  -J-  b  OC  (Par.  59)  ;  and, 
consequently,  the  total  apparent  reluctance  of  the  armature 
takes  the  form  x  -\-y&,  and  the  useful  flux  passing  through 

or 

the    armature     $   =  ,   &,    being     the    magnetomo- 

x  ~r  y  v 

tive  force  in  gilberts,  but  £F,  may  be  expressed  in  ampere- 
turns,  in  amperes  or  in  volts  applied  to  the  coils. 

254.  When  the  characteristic  curves  of  a  shunt  machine  have 
been   obtained,  it  is  a  simple   matter  to  determine  what  the 
series  winding  must   be   in    order  to  properly   compound   it, 
either  for  the  drop  in  the  armature,  or  for  the  drop  in  any 
given  portion  of  the  external  circuit  as  well.     Thus,  suppose  it 
be  required  to  determine  the  series  winding  for  the  machine 
whose  characteristic  curve  is  represented  in  Fig.  168.     If  the 
E.  M.  F.  required  at  the  terminals  of  the  machine  be  120  volts 
at  all  loads,  and  if  the  drop  in  the  armature,  due  to  its  resistance 
at  full  load,  as  well  as  the  resistance  of  its  series  coil,  and  to 
any  shifting  of  the  brushes  that  may  be  necessary,  amounts  in 
all  to   10   volts,   then    the  full-load    current  must  supply  the 
M.  M.  F.  necessary  to  carry  the    E.  M.  F.  from   120  to   130 
volts,  equivalent  to  raising  the  pressure  by  8  volts  from.  70 
to  78  volts  on  the  shunt  winding.     The  increase  in  current 
strength  from  the  shunt  winding  represented  by  these  eight 
volts  multiplied  by  the  number  of  turns  in  the  shunt  winding, 
gives  the   M.  M.  F.  required,  and  the  full-load   current  must 


214  ELECTRO-DYNAMIC  MACHINERY. 

pass    through   a   sufficient    number   of   turns    to    supply   this 
M.  M.  F.  in  its  series  coil. 

255-  In  a^  commercial  circuits,  electro-receptive  devices 
require  to  be  operated  either  at  Constant  current  or  at  constant 
pressure.  The  majority  of  such  devices  are  designed  for  con- 
stant pressure;  such,  for  example,  are  parallel  or  multiple- 
connected  incandescent  lamps  and  motors.  Some  devices, 
however,  require  to  be  operated  by  a  constant  current.  Of 
these,  the  arc  lamp  is,  perhaps,  the  most  important.  Series- 


FIG.    169. — SHUNT    FIELD    AND    RHEOSTAT. 

connected  incandescent  lamps,  and  a  few  forms  of  motors,  also 
belong  to  this  class. 

256.  In  order  to   maintain  a  constant  pressure  at  the  ter- 
minals of  a  motor  with  a  varying   load,   it  is   necessary,   in 
order  to  compensate  for  the  drop  of  pressure  in  supply  con- 
ductors, that  the  pressure  at  the  generator  terminals  either  be 
kept  constant,  or  slightly  raised  as  the  load  increases.     With 
shunt-wound  machines  this  regulation  requires  to  be  carried 
out  by  hand,  a  rheostat  being  inserted  between  the  field  and 
the  armature,  as  shown  in  Fig.  169. 

257.  Various  forms  are  given  to  rheostats  for  such  purposes. 
They  consist,  however,  essentially  of  coils  of  wire,  usually  iron 
wire,  so  arranged  as  to  expose  a  sufficiently  large  surface  to 
the  surrounding  air,  as  to    enable  them  to  keep  within  safe 
limits  of  temperature  under  all  conditions  of  use.     The  resist- 
ance is  divided  into  a  number  of  separate  coils  and  the  ter- 
minals of  these  are  connected  to  brass  plates  usually  arranged 


REGULATION-  OF  DYNAMOS. 


215 


in  circles,  upon  the  external  surface  of  a  plate  of  slate,  wood 
or  other  non-conducting  material,  so  that,  by  the  aid  of  a 
handle,  a  contact  strip  can  be  brought  into  connection  with 
any  one  of  them.  The  coils  being  arranged  in  series,  the 
movement  of  the  handle  in  one  direction  adds  resistance  to  the 
field  circuit,  and  in  the  opposite  direction,  cuts  resistance  out 


FIGS.    170  AND    171. — FORMS   OF  FIELD   RHEOSTAT. 

of  the  circuit.  Figs.  170  and  171  show  different  forms  of  field 
rheostats,  with  wheel  controlling  handles.  In  some  rheostats 
the  resistance  wire  is  embedded  in  an  enamel,  which  is  caused 
to  adhere  to  a  plate  of  cast  iron.  This  gives  a  very  compact 
form  of  resistance  ;  for,  the  intimate  contact  of  the  wire  with 
the  iron  plate,  together  with  the  large  free  surface  of  the  plate, 
enables  the  heat  to  be  readily  dissipated  and  prevents  any 
great  elevation  of  temperature  from  being  attained.  Two  of 
such  rheostats  are  shown  in  Fig.  172. 


258.  Compound-wound   machines   can  be  made  to  regulate 
automatically,  and   do   not  require   to   have   their  E.   M.   F. 


2i6  ELECTRO-DYNAMIC  MACHINERY. 

adjusted  by  the  aid  of  a  field  rheostat.     For  this  reason  they 
are  very  extensively  used  in  the  operation  of  electric  motors. 

Series-wound  machines  are  invariably  used  for  operating  arc 
lamps  in  series.  Since  the  load  they  have  to  maintain  is  apt 
to  be  variable,  such  machines  must  possess  the  power  of  vary- 
ing their  E.  M.  F.  within  wide  limits.  Two  methods  are  in  use 
for  maintaining  constant  the  strength  of  current.  That  in  most 
general  use  is  to  shift  the  position  of  the  collecting  brushes  on 
the  commutator  so  as  to  take  off  a  higher  or  lower  E.  M.  F. 
according  as  the  load  in  the  external  circuit  increases  or  de- 
creases. The  effect  of  this  shifting  will  be  evident  from  an 
inspection  of  Fig.  156  ;  for,  if  the  diameter  of  commutation  be 


FIG.     172. — ENAMEL   RHEOSTATS. 

shifted  to  the  right  or  left,  the  E.  M.  F.  in  some  of  the  coils- 
will  be  opposed  to  that  in  the  remainder,  the  difference  only 
being  delivered  at  the  brushes.  In  practice,  the  diameter  of 
commutation  would  never  reach  the  position  of  maximum  E. 
M.  F.  represented  in  Fig.  156,  and  might,  on  the  other  hand, 
rotate  through  a  sufficiently  large  angle  to  produce  only  a  small 
fraction  of  the  total  E.  M.  F.  - 

259.  In  all  cases  where  the  brushes  are  shifted  through  a 
considerable  range  over  the  commutator,  care  has  to  be  taken 
to  avoid  the  sparking  that  is  likely  to  ensue  if  a  certain  balance 
is  not  maintained  between  the  M.  M.  F.  of  the  armature  and 
the  magnetic  intensity  in  the  air-gap.  The  fact  that  the  current 
strength  through  the  armature  coils  is  practically  constant  at 


REGULATION   OF  DYNAMOS.  217 

all  loads,   enables  this  balance   to   be    effectually  maintained, 
when  once  it  has  been  reached  at  any  load. 

260.  Series-wound  arc-light  generators  have  their  armatures 
wound  in  two  ways  ;  namely,  closed-coil  armatures,  and  open-coil 
armatures.  In  the  former,  all  the  armature  coils  are  constantly 
in  the  circuit,  while  in  the  latter,  some  of  the  coils  are  cut  out 
of  the  circuit  by  the  commutator,  during  a  portion  of  the  revo- 
lution. The  ordinary  continuous-current  generator  for  pro- 
ducing constant  pressure  is,  therefore,  a  closed-coil  armature. 
Fig.  173  represents  diagrammatically  a  form  of  open-coil  arma- 
ture winding.  The  three  coils  shown  are  ooanected  to  a  com- 


FIG.     173. — OPEN   COIL-WINDING. 

mon  or  neutral  point  o.  In  the  position  represented,  the  coil 
A,  is  disconnected  from  the  circuits,  the  coils  B  and  C,  remain- 
ing in  the  circuit  of  the  brushes  b  b' . 

261.  In  closed-coil,  series-wound,  arc-light  generators,  the 
brushes  are  given  a  forward  lead ;  i.  e.,  a  lead  in  the  direction  of 
the  rotation  of  the  armature.  The  amount  of  this  lead  controls 
the  E.  M.  F.  produced  between  the  brushes.  It  is  essential,  in 
order  to  prevent  violent  sparking,  that  the  coil  under  commuta- 
tion should  be  running  through  an  intensity  sufficient  to  nearly 
reverse  the  current  in  the  commuted  coil  during  the  time  of  its 
short  circuiting.  Since  the  current  strength  in  the  field,  and 
also  in  the  armature,  is  maintained  constant  at  all  loads,  it  is 
necessary  that  the  intensity  of  flux,  through  which  the  com- 
muted coils  run,  should  be  uniform,  or  nearly  uniform,  at  all 
loads  and  of  the  proper  degree  to  effect  current  reversal.  The 


2l8 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


M.  M.  F.  of  the  field  magnet,  is  constant  and  the  M.  M  F.  of  the 
armature  is  also  constant,  but  the  flux  produced  by  the  M.  M. 
F.  of  the  armature  varies  with  the  position  of  the  brushes  and 
the  number  of  active  turns  that  exist  in  that  portion  of  the  arma- 
ture which  is  covered  by  the  pole-piece,  on  each  side  of  the  diam- 
eter of  commutation.  The  pole-pieces  are  usually  so  shaped 
that  as  the  number  of  active  turns  in  the  armature  covered  by 
each  pole  increase  ;  /.  e.,  as  the  load  and  E.  M.  F.  of  the 
machine  increase,  the  trailing  pole  corners  become  more  nearly 
saturated,  and  by  their  increasing  reluctance  check  the  tendency 
to  increase  the  flux  from  the  armature,  so  that  an  approximate 
balance  between  the  field  flux  and  the  armature  flux  is  main- 


.FIG.   174. — DIAGRAM    OF    AUTOMATIC   REGULATOR   CONNECTIONS. 

tained  at  all  loads.  The  armature  flux  always  opposes  the  field 
flux  at  the  diameter  of  commutation.  The  magnetic  circuit, 
therefore,  has  to  be  so  designed  that  the  armature  flux  shall 
never  quite  neutralize  the  field  flux  at  this  point,  but  shall 
always  leave  a  small  residual  field  flux  for  the  purpose  of  obtain- 
ing sparkless  commutation. 

262.  The  other  method,  which  is  employed  for  maintaining 
the  current  strength  constant,  introduces  a  variable  shunt 
around  the  terminals  of  the  field  coil,  in  such  a  manner  that 
when  the  current  through  the  circuit  becomes  excessive,  the 
shunt  is  lowered  in  resistance,  and  diverts  a  sufficiently  large 
amount  of  current  from  the  field  magnets  to  lower  their  M.  M 
F.  to  the  required  value.  In  order,  however,  to  avoid  the 
necessity  for  making  this  regulation  by  hand,  it  may  be  effected 


REGULATION  'OF  DYNAMOS.  219 

automatically  as  follows  :  namely,  an  electromagnet,  situated 
in  the  main  circuit,  is  caused  by  the  attraction  of  its  armature, 
on  an  increase  in  the  main  current  strength,  to  bring  pressure 
upon  a  pile  of  carbon  discs.  This  pile  of  discs  offers  a  certain 
resistance  to  the  passage  of  a  current,  the  resistance  of  the  pile 
diminishing  as  the  pressure  upon  it  increases.  The  pile  is 
placed  as  a  shunt  around  the  field  magnet,  so  as  to  divert  from 
the  magnet  a  portion  of  the  main  current  strength.  When  the 
attraction  on  the  armature  of  the  electromagnet  increases  the 
pressure  on  the  pile,  the  resistance  of  the  shunt  path  is  dimin- 
ished, and  less  current  flows  through  the  field  magnets,  as 
represented  in  Fig.  174,  where  -S",  is  the  series  winding,  shunted 
by  the  carbon  pile  P,  and  Mt  is  the  controlling  magnet  inserted 
in  the  main  circuit. 

263.  Both  the  above  methods  are  capable  of  compensating 
not  only  for  variations  in  the  resistance,  or  C.  E.  M.  F.  of  the 
circuit,  but  also  for  variations  in  the  speed  of  driving.  In  this 
respect  the  compensation  is  more  nearly  complete  than  that 
of  constant  pressure  machines;  for,  compound-wound  gener- 
tors  can  maintain  a  constant  pressure  under  variations  of  load, 
but  not  under  variations  of  speed. 


CHAPTER    XXI. 

COMBINATIONS   OF    DYNAMOS   IN    SERIES   OR    IN    PARALLEL. 

264.  When  a  system  of  electric  conductors  is  supplied  from 
a  central  station,  it  is  evident,  that  if  the  load  on  the  system 
was  constant,    a    single  large    generator  unit  would   be   the 
simplest  and  cheapest  source  of  electric  supply,  except,  per- 
haps, on  the  score  of  reserve,  in  case  of,  accidental  breakdown. 
In  practice,  however,  the  load  is  never  constant,  and,  there- 
fore, the  capacity  of  the  generating  unit  is  always  consider- 
ably less  than  the  total  activity  that  has  to  be  supplied  at  the 
busiest  time.     Moreover,   engines  and  generators  are  neces- 
sarily so  constructed,    that  while  they  may  be  comparatively 
very  efficient  when  working  at  full  load,  they  are  far  less  effi- 
cient when  working  at  a  small  fraction  of  their  load,  so  that  it 
is  desirable  to  maintain  such  units  as  are  in  use,  at  full  load 
under  all  circumstances.     This  consideration  of  wasted  power, 
in  operating  large  units  at  light  loads,  applies  with  less  force 
to  plants  operated  by  water  power,  but,  even  in  this  case,  it  is 
usually  found  uneconomical  to  operate  a  large  generator,  for 
many  hours  of  a  day,  when  a  smaller  one  would  be  quite  com- 
petent to  supply  the  load. 

265.  The  generating  units  in  a  central  station  are,  there- 
fore, so  arranged  that  they  may  be  individually  called  upon  at 
any  time  to  add   their  activity  to  the  output  of  the  station. 
Electrically,  these   generators   must   be   connected   either   in 
separate  circuits,  or  in  series  or  in  parallel  in  the  same  circuit. 

The  method  of  connecting  dynamos  in  series,  so  far  as  con- 
tinuous-current circuits  are  concerned,  is  only  employed  for 
arc  lamps  operated  in  series.  When  a  great  number  of  arc 
lamps  have  to  be  supplied  over  a  given  district,  they  are  usu- 
ally arranged  in  different  circuits,  each  circuit  containing  ap- 
proximately the  same  number  of  lamps.  Each  such  circuit  is 
then  connected,  as  a  full  load,  to  a  single  arc-light  generator. 


DYNAMOS  IN  SERIES   OR   IN  PARALLEL.  221 

When,  however,  owing  to  some  failure  of  continuity  in  a  cir- 
cuit, it  is  found  impossible  to  operate  two  circuits  independ- 
ently, it  is  sometimes  desirable  to  connect  the  two  circuits  to- 
gether at  some  point  outside  the  station,  and  to  operate  the 
increased  load  of  lamps  by  two  or  more  dynamos  connected  in 
series. 

266.  Generators  are  also  connected  in  series  when  it  is  de- 
sired to  employ,  on  the  external  circuits,  the  sum  of  the  pres- 
sures of  those  generators.     For  example,  in  cases  of  the  trans- 
mission of  power  to  considerable  distances,  a  high  pressure  in 
the  conducting  circuit  is  economically  necessary.     Whenever 
this  pressure  is  greater  than  that  which  can  be  readily  obtained 
from  a  single  continuous-current  generator,  it  is  possible  to 
connect  two  or  more  generators  in  series,  so  as  to  obtain  the 
sum  of  their  pressures.     Thus,  five  generators,  each  supplying 
500  volts   pressure,   will,  when  connected  in   series,    supply  a 
total  pressure  of  2,500  volts.     The  plan  is  rarely  followed. 

267.  As  a  modification  of  the  above  plan,  which  is  rarely 
adopted,  five-wire,  and  three-wire  systems,  employing  respec- 
tively four  and  two  generators  in  series,  are  in  use.     The  five- 
wire  system,   although  employed  in  Europe,   has  not   found 
favor  in  the  United  States.     The  three-wire  system,  however, 
is  extensively  employed.     In   this   system,   two  generators  of 
equal  voltage,  say  125   volts,  are   connected  in  series  so  as  to 
supply  a  total  pressure  of  250  volts.     Such  a  pressure  is  cap- 
able of  operating  incandescent  lamps  in  series  of  two.     To 
enable  single  lamps,  however,  to  be  operated  independently,  a 
third  or  neutral  wire  is  carried    through  the  system  from  the 
common  connection  point  of  the  two  generators,  and  the  dis- 
tribution of  lamps,  on  the  two  sides  of  the  system,  is  so  arranged 
that  the  equalizing  current,  passing  through  the  neutral  wire,  is 
small,  and  nearly  as  many  lamps  are  operated  at  any  one  time 
on  the  positive,  as  on  the  negative  side  of  the  system.     A  pair 
of  generators  connected  for  three-wire  service,  therefore,  con- 
stitutes a  generating  unit  in  a  three-wire  central  station. 

268.  Series-generators  are  never,  in  practice,  connected  in 
parallel.       Shunt-wound  and  compound-wound    machines   are 
capable  of  being  connected  in  parallel,  and   most  central  sta- 


222  ELECTRO-DYNAMIC  MACHINERY. 

tions  arrange  the  generators  in  such  a  manner  that  they  may 
be  connected  to,  or  disconnected  from,  the  mains  according  to 
the  requirements  of  the  load. 

269.  Central  stations,  supplying  incandescent  lamps  in  par- 
allel,  usually  employ  shunt-wound  generators,  for  the  reason 
that  the  efficient  and  economic  operation  of  the  lamps  requires 
a  nearly  uniform  pressure  at  all  lamp  terminals. 

Not  only  does  the  uniformity  in  the  amount  of  illumination 
from  an  incandescent  lamp  depend  upon  the  uniformity  of  the 
pressure  supplied  at  its  terminals,  very  small  variations  in  the 
pressure  markedly  varying  the  intensity  of  light,  but  also  such 
variations  of  pressure  materially  affect  the  life  of  the  lamp. 
Thus  a  5o-watt,  16  candle-power,  incandescent  lamp,  intended  to- 
be  operated  at  a  pressure  of  115  volts,  would  have  its  probable 
life  reduced  by  about  15  per  cent.,  if  operated  steadily  at  116 
volts,  and  reduced  by  about  30  per  cent,  if  operated  steadily 
at  117  volts  pressure.  For  this  reason  the  pressure  in  the 
street  mains  supplying  the  lamps  requires  constant  careful  at- 
tention. Since  it  would  be  impossible  to  obtain  at  the  mains 
a  sufficient  uniformity  of  pressure,  under  all  conditions  of  load, 
by  compound  winding,  and  hand  regulation  would  still  be  re- 
quired, there  is  an  advantage  in  dispensing  altogether  with, 
compound  winding,  and  resorting  to  hand  regulation,  with 
shunt  winding,  for  the  entire  adjustment. 

270.  When  two  or  more  generators  are  connected  in  parallel, 
it  becomes  necessary  that  the  electromotive  forces  they  supply 
shall  be  equal,  within   certain   limits.      If,   for  example,    two- 
generators  are  connected  in  parallel,  each  working  at  half  load, 
then  if  the  drop  of  pressure  in  each  generator  armature  at  full 
load  is  two  per  cent,  of  its  total  E.  M.  F.,  it  is  evident  that  it 
is  only  necessary  to  increase  the  pressure  of  one  generator  twa 
per  cent,  above  that  of  the  other,  in  order  that  the  pressure  at 
the  brushes  of  the  first  shall  be  equal  to  the  E.  M.  F.  generated 
in  the  armature  of  the  second.      Under  these  circumstances  na 
current  will  flow  through  the  armature  of  the  second  machine, 
and  all  the  load  will  be  thrown  on  the  first  machine.     If  the 
E.  M.  F.  of  the  first  machine  be  still  further  raised,  the  pres- 
sure at  its  brush-es-will  be  greater  than  the  E.  M.  F.  in  the 


DYNAMOS  IN  SERIES   OR  IN 


armature  in  the  second,  and  a  current  will  pass  through  the 
second  armature  in  a  direction  opposite  to  that  which  it  tends 
to  produce,  and,  therefore,  in  a  direction  tending  to  rotate  the 
second  generator  as  a  motor.  In  other  words,  the  control  of 
pressure  between  the  two  machines  must  be  within  closer 
limits  than  two  per  cent.  Early  in  the  history  of  central 
station  practice,  difficulties  were  experienced  in  controlling 
the  pressure  of  multiple-connected  dynamos  within  limits  nec- 
essary to  avoid  this  unequalizing  action,  but  at  the  present 
time,  the  governing  of  the  engines  and  the  control  of  the  field 
magnets  are  so  reliable,  that  this  difficulty  has  practically  dis- 
appeared. It  is  important  to  remember,  however,  that  the 
larger  the  generator  unit  employed,  and  the  smaller  the  drop 
in  pressure  taking  place  at  full  load  through  its  armature,  the 
narrower  is  the  limit  of  speed  or  regulation,  in  which  inde- 
pendent units  will  equalize  their  load,  although  as  a  counter- 
acting tendency,  the  larger  will  be  the  amount  of  power  which, 
in  case  of  disequalizing,  will  be  thrown  upon  the  leading  ma- 
chine tending  to  check  its  acceleration. 

271.  Compound-wound  generators  are  almost  invariably  em- 
ployed for  supplying  electric  currents  to  street  railway  sys- 
tems. This  is  principally  for  the  reason  that  the  load  in  a 
street  railway  system  is  necessarily  liable  to  sudden  and  marked 
fluctuations,  and  these  fluctuations  would  be  liable  to  produce 
marked  variations  in  the  pressure  at  the  generator  terminals,  if 
the  machines  were  merely  shunt  wound.  Such  generators  are 
operated  in  parallel  units.  Here,  as  in  the  case  of  shunt- 
wound  machines,  it  is  necessary  that  the  E.  M.  F.  generated 
by  each  machine  should  be  nearly  the  same,  in  order  that  the 
load  should  be  equally  distributed;  but  instability  of  control  is 
greater  in  the  case  of  compound-wound  machines  than  in  the 
case  of  shunt  machines,  for  the  reason  that  when  one  of  a 
number  of  parallel-connected  shunt-wound  machines  acceler- 
ates, and  thereby  rises  in  E.  M.  F.,  so  as  to  assume  an  undue 
share  of  the  load,  the  drop  in  the  armature  thereby  increases, 
and  tends  to  diminish  the  irregularity,  so  that  not  only  does 
the  greater  load  tend  to  retard  the  engine  connected  to  the 
leading  machine,  but  also  the  drop  in  its  armature  aids  in 
equalizing  the  distribution. 


224 


ELECTRO-D  Y NAM  1C  MA  CHINER  Y. 


In  the  case  of  compound-wound  machines  in  parallel,  any 
acceleration  tends,  as  before,  to  increase  the  E.  M.  F.  of  the 
generator  and,  therefore,  its  share  of  the  load,  but  the  series 
coil  of  the  compound  winding  being  excited  by  the  additional 
load,  tends  to  increase  the  output  of  the  machine,  and,  there- 
fore, the  governing  of  the  engine  has  to  be  entirely  depended 
on  to  prevent  disequalization.  Of  recent  years,  however,  the 
plan  has  been  widely  adopted  of  employing  an  equalizing  bar 
between  compound-wound  generating  units  operated  in  par- 


f  1 


B  B 

FIG.    175. — PARALLEL    CONNECTION    OF    COMPOUND-WOUND    GENERATORS. 


allel.  The  connections  of  an  equalizing  bar  are  shown  in  Fig. 
.175.  Here  the  two  compound-wound  generators  are  connected 
to  the  positive  and  negative  omnibus  bars,  or  bus  bars,  as  they 
are  generally  termed,  AA  and  BB,  while  the  series  coils  are 
connected  together  in  parallel  by  the  equalizing  bar  QQ.  It 
is  evident  that  the  equalizing  bar  connects  all  series  coils  of 
the  different  dynamos  in  parallel,  so  that  any  excess  of  current, 
supplied  by  the  armature. of  one  machine,  must  necessarily  ex- 
cite all  the  generators  to  the  same  extent. 

272.  When  a  number  of  compound-wound  generators  are 
running  in  parallel,  and  the  load  increases,  so  that  it  is  desired 
to  add  another  unit  to  the  generating  battery  of  dynamos,  the 
engine  connected  with  the  new  unit  is  brought  up  to  speed, 
and  the  shunt  field  excited.  This  brings  the  E.  M.  F.  of  the 


DYNAMOS  IN  SERIES  OR   IN  PARALLEL.  225 

machine  up  to  nearly  500  volts.  Its  series  winding  is  then 
connected  in  parallel  with  the  series  winding  of  the  neighbor- 
ing machines,  by  the  switch  on  the  equalizing  bar,  so  that  its 
excitation  is  then  equal  to  that  of  all  the  other  machines.  The 
E.  M.  F.  of  the  machine  is  then  brought  up  slightly  in  excess 
of  the  station  pressure  by  the  aid  of  the  field  rheostat,  and,  as 
soon  as  this  is  accomplished,  the  main  armature  switch  is  closed, 
thus  connecting  the  armature  with  the  bus  bars.  The  load  of 
the  machine  is  finally  adjusted  by  increasing  the  shunt  excita- 
tion, with  the  aid  of  the  rheostat,  until  the  ammeter  connected 
with  the  machine  shows  that  its  load  is  approximately  equal  to 
that  of  the  neighboring  generators.  The  same  steps  are  taken 
in  reverse  order  to  remove  a  generator  from  the  circuit. 

273.  Fig.  176  is  a  diagram  of  a  street-railway  switchboard 
for  two  generators.  It  is  customary,  both  for  convenience 
and  simplicity,  to  erect  switchboards  in  panels,  one  for  each 
generating  unit,  so  that  each  panel  controls  a  separate  unit, 
and  is  in  immediate  connection  with  its  neighbors.  In  the 
figure,  the  two  panels  are  designated  by  dotted  lines,  the  one 
on  the  left,  active,  and  the  one  on  the  right,  out  of  use.  On 
each  panel  there  are  two  main  switches,  P  and  JV,  for  the  posi- 
tive and  negative  armature  terminals.  A  smaller  switch,  not 
shown,  is  usually  located  on  the  right  of  each  panel,  and  is  for 
lighting  up  the  station  lamps  from  any  panel  and  its  connected 
machines,  at  will.  R,  is  a  shunt  rheostat,  placed  at  the  back  of 
the  panel,  with  its  handle  extending  through  to  the  front,  and 
S,  is  a  small  switch  for  opening  and  closing  the  shunt  circuit  of 
the  field  coils  through  the  rheostat,  1?.  A,  is  the  generator 
ammeter,  brought  into  use  by  the  switches  P  and  JV,  and  T, 
is  the  automatic  circuit-breaker  for  the  panel.  This  electro- 
magnetic circuit-breaker,  opens  the  circuit  of  the  machine 
when  the  current  strength,  owing  to  a  short  circuit  or  other 
abnormal  condition,  becomes  dangerously  great,  thereby  reliev- 
ing the  generator  of  the  strain.  The  switch  connected  to  the 
equalizing  bar  E  is  not  placed  in  this  instance,  on  the  panel, 
but  is  mounted  close  to  the  generator  with  the  object  of 
diminishing  the  amount  of  copper  conductor  required.  Each 
panel  is  also  provided  with  a  voltmeter  connection  and  lightning 
arrester,  which  have  been  omitted  here  for  the  sake  of  simplicity. 


226 


EL  E  C  TR  0-D  YNA  MIC  MA  CHINER  Y. 


274.  The  operations  for  introducing  a  unit  into  the  battery 
of  generators  in  this  case,  is  as  follows :  the  generator  is  brought 
up  to  speed,  the  equalizing  switch  is  closed,  %thus  connecting 
the  series  coils  of  the  machines  in  parallel  with  the  machines 
in  use.  The  positive  main  switch  P,  is  next  closed,  connecting 


£ 


V EQUALIZING  BUS 

FIG.   176. — DIAGRAM   OF   SWITCHBOARD   CONNECTIONS   FOR   TWO    COMPOUND- 
WOUND    GENERATORS. 


one  side  of  the  armature  to  ground  and  to  return  track  feeders. 
The  field  switch  S,  is  next  closed,  and  the  E.  M.  F.  of  the 
machine  brought  up  to  slightly  above  station  pressure  by  the 
aid  of  the  rheostat  R  ;  finally,  the  negative  main  switch  N,  is 
closed,  throwing  the  armature  into  the  battery,  and  the  load  is 


DYNAMOS  IN  SERIES  OR   IN  PARALLEL.  22^ 

adjusted  by  the  rheostat  R,  in  accordance  with  the  indications 
of  the  ammeter  A. 

275«  Another  arrangement  for  railway  switchboards  consists 
in  mounting  the  three  switches,  in  close  proximity  to  each 
other  and  attaching  a  single  handle  to  the  three  blades,  so  that 
the  three  connections  may  be  made  or  broken  by  a  single 
operation. 

When  the  railway  mains  are  connected  with  the  station  by 
several  feeders,  it  is  customary  to  add  another  section  to  the 
switchboard  where  switches  and  ammeters  are  provided  for 
handling  the  various  feeders. 


CHAPTER  XXII. 

DISC  ARMATURES    AND    SINGLE-FIELD-COIL  MACHINES. 

276.  Before  leaving  the  subject  of  generators,  it  may  be  well 
to  discuss  a  few  types  of  generators  that  do  not  fall  under  the 


4  FIG.   177.— DISC-ARMATURE    GENERATOR. 

types  already  discussed,  and  which  are  occasionally  met  with 
in  practice. 

These  may  be  described  as  ; 

(i.)  Disc-armature  machines. 

(2.)  Single-field-coil  machines. 

228 


FIG.   178. — DISC   ARMATURE. 


230  ELECTRO-DYNAMIC  MACHINERY, 

(3.)  Unipolar  machines,  or  commutatorless  continuous- 
current  machines. 

277.  Generators  employing  disc  armatures  are  frequently 
used  in  Europe,  and  although  they  are  very  seldom  employed 
in  the  United  States,  yet  it  is  proper  to  describe  them  as  being 
types  of  machines  capable  of  efficient  use.  In  one  form  of 
disc-armature  generator,  the  armature  is  devoid  of  iron,  and  is 
built  of  conducting  spokes  like  a  wheel,  which  revolves  in  a 
vertical  plane  between  opposite  field-magnet  poles.  Such  a 


•    ,.        FIG.   179. — DIAGRAM   OF   DISC-ARMATURE   WINDING. 

disc-armature  machine  is  shown  in  Fig.  177.  It  is  to  be 
observed  that  the  entire  machine  is  practically  encased  in  iron, 
and  is  provided  with  three  windows  on  the  vertical  face; 
through  these  windows  the  brushes,  BB,  rest  on  the  commu- 
tator which  is  placed  on  the  periphery  of  the  disc,  resembling 
in  this  respect  the  generator  in  Fig.  103.  The  armature  of  this 
machine  is  shown  in  Fig.  178  mounted  on  a  suitable  support. 
The  radial  spokes  are  of  soft  iron,  and  are  connected  into  loops 
by  the  copper  strips  leading  to  the  commutator  segments  on 
the  periphery.  The  object  of  employing  iron  spokes  is  to 
diminish  the  reluctance  of  the  air-gap.  The  field  poles  face 


DISC  ARMATURES. 


231 


each  other,  being  separated  by  the  disc  armature,  which 
revolves  between  them.  Such  an  armature  is  evidently  capa- 
ble of  being  operated  at  an  abnormally  high  temperature 
without  danger,  being  constructed  of  practically  fireproof 
materials.  The  electric  connections  of  an  octopolar  machine 
are  represented  diagrammatically  in  Fig.  179.  The  brushes,  it 
will  be  observed,  are  applied  at  the  centres  of  any  adjacent 


FIG.   ISO. — DISC-ARMATURE   GENERATOR. 

pair  of  poles.     Another  form  of  the  machine  is  represented  in 
Fig.  1 80. 

278.  An  example  of  a  single-field-coil  multipolar  dynamo  is 
shown  in  Fig.  181.  This  is  a  quadripolar  generator  with  four 
sets  of  brushes.  The  interior  of  the  field  frame,  with  its  pro- 
jecting pole-pieces  and  exciting  coil,  is  shown  in  Fig.  182. 
It  will  be  seen  that  the  field  frame  is  made  in  halves, 


FIG,   l8l. — COMPOUND-WOUND    GENERATOR  WITH   SINGLE   FIELD    COIL. 


FIG.   182. DETAILS    OF    MAGNET,  SINGLE-FIELD-COIL    GENERATOR. 


SINGLE-FIELD-  COIL  MA  CHINES.  • 


233 


between  which  are  enclosed  the  armature  and  the  single  field 
magnetizing  coil.  Four  projections  N,  N,  and  Sy  S,  form  the 
pole-pieces  of  the  quadripolar  field;  that  is  to  say,  the  magnetic 


FIG.   183. — ARMATURE   OF   QUADRIPOLAR,  SINGLE-FIELD-COIL   MACHINE. 

flux  produced  by  the  M.  M.  F.  of  the. single  coil  C  C,  passes 
through  the  field  frame  into  the  two  pole  faces  JV  and  JV,  in 
parallel  through  the  armature  into  the  adjacent  pole  faces 
S,  S,  thus  completing  the  circuit  through  the  field  frame.  The 
drum-wound,  toothed-core  armature,  is  shown  in  Fig.  183. 


CHAPTER  XXIII. 

COMMUTATORLESS    CONTINUOUS-CURRENT  GENERATORS. 

279.  Commutatorless  continuous-current  dynamos  are  sometimes 
called  unipolar  dynamos,  although  erroneously.  It  is  impossible 
to  produce  a  single  magnetic  pole  in  a  magnet,^  since  all  mag- 
netic flux  is  necessarily  circuital,  and  must  produce  poles,  both 
where  it  enters  and  where  it  leaves  a  magnet.  The  fact  that 
these  machines  are  capable  of  furnishing  a  continuous  current 
without  the  aid  of  a  commutator,  at  one  time  caused  consider- 
able study  to  be  given  to  them  in  the  hope  of  rendering  them 


FIG.   184. — FARADAY    DISC. 

commercially  practicable.  The  maximum  E.  M.  F.  which  they 
have  been  constructed  to  produce,  appears,  however,  to  have 
been  about  six  volts,  and,  consequently,  they  have  practically 
fallen  out  of  use,  although  they  have  been  commercially 
employed  for  electroplating. 

280.  Fig.  184  represents  what  is  known  as  a  Faraday  disc. 
This  was,  in  fact,  the  earliest  dynamo  ever  produced,  and  was 
of  the  so-called  unipolar  type;  for  here,  a  copper  disc  D, 
rotated,  by  mechanical  force,  about  an  axis  parallel  to  the 
direction  of  the  magnetic  flux,  supplied  by  a  permanent  horse- 
shoe magnet  M  M,  continuously  cuts  magnetic  flux  in  the  same 


CONTINUOUS-CURRENT  GENERATORS.  235 

direction,  and,  consequently,  furnishes  a  continuous  E.   M.   F. 
between  the  terminals  S,  S',  without  the  use  of  a  commutator. 

281.  The  portion  of  the  disc  lying  between  the  poles  is  caused 
to  rotate  in  a  nearly  uniform  magnetic  flux,  and  with  a  velocity 
which  depends  upon  the  radius  of  the  disc  at  the  point  con- 
sidered, as  well  as  on  the  angular  speed  of  rotation.  The  di- 
rection of  the  E.  M.  F.  induced  will  be  radially  downward  from 
the  axis  to  the  periphery,  and,  if  connection  be  secured  between 
the  axis  as  one  terminal,  and  the  rotating  contact  or  brush  as 
the  other  terminal,  an  E.  M.  F.  will  be  continuously  produced  in 
that  portion  of  the  disc  which  lies  beneath  the  poles;  or,  more 
strictly,  in  that  portion  of  the  disc  which  passes  through  the 
flux  between  them  and  around  their  edges.  If,  however,  as  in 
Fig.  185,  the  disc  be  completely  covered  by  the  pole  faces,  a 


FIG.    185. — FARADAY    DISC. 

radial  system  of  E.  M.  Fs.  will  be  induced  outward  in  the  direc- 
tions indicated  by  the  arrows,  or  inward,  if  the  direction  of 
rotation  be  reversed.  If  no  contacts  are  applied  to  the  disc, 
these  E.  M.  Fs.  will  supply  no  current,  and  will  do  no  work. 
If  brushes  are  applied  at  the  axis,  and  at  any  or  all  parts  of 
the  periphery,  the  E.  M.  F.  can  be  led  off  to  the  external  circuit. 

282.  The  value  of  the  E.  M.  F.  will  depend  upon  the  angular 
speed  of  rotation,  the  intensity  of  the  magnetic  flux,  and  the 
radius  of  the   disc.     The  intensity  of  the  magnetic  flux  can 
usually  be  made  much  greater  by  the  use  of  a  soft-iron  disc 
instead    of  a   copper  disc,    thereby  practically    reducing    the 
reluctance  of  the  magnetic  circuit  between  the  poles  to  that 
of  two  clearance  films  of  air,  since  the  reluctance  of  the  iron 
disc  will  be  negligibly  small. 

283.  If  we  consider  any  small  length  of  radius  d  /,  Fig.  186, 
situated  ,at  a  distance  /,  from  the  axis.of  the  disc,  the  E.  M.  F. 


236  ELECTRO-DYNAMIC  MACHINERY. 

generated  in  this  element  of  the  disc  will  be  the  product  of  the 
intensity,  the  length  of  the  element,  and  its  velocity  across  the 
flux.  The  element  will  be  moving  across  the  magnetic  flux  of 
uniform  intensity,  (B  gausses,  at  a  velocity  /  co  centimetres  per 
second,  where  GO,  is  the  angular  velocity  of  the  disc  in  radians 
per  second.  Consequently,  the  E.  M.  F.  in  this  element  will  be: 

de  —  I  &o  .  dr  .  B  C.  G.  S.  units  of  E.  M.  F. 

The  total  E.  M.  F.  will  be  the  sum  of  the  elementary  E.  M.  Fs. 
included  in  the  radius  taken  from  /  =  0,  to  /  =  Z,  the  radius 
of  the  disc,  or  the  integral  of  de,  in  the  above  equation  between 

Za 

the  limits  /  =  o,  and  /  =  L.      This  integral  is  —  GO  (&  =  e. 

The  E.  M.  F.  from  such  a  disc,  therefore,  increases  as  the 


FIG.  i 86 

square  of  the  radius  of  the  disc,  directly  as  the  speed,  and 
directly  as  the  uniform  intensity  of  the  magnetic  flux.  The 
same  result  can  be  obtained  in  a  slightly  different  expression, 
since  G?  =  2  n  «,  where  «,  is  the  number  of  revolutions  of  the 

Z8 
disc  in  a  second,  e  —  —  .  27rn(&  =  7rZ,'tn(&=:Sn($>  where 

2 

S,  is  the  active  surface  of  the  disc.  This  will  also  be  true  if 
the  surface  S,  instead  of  extending  over  the  entire  face  of  the 
disc,  extends  only  from  the  periphery  to  some  intermediate 
radius.  From  this  point  of  view  the  E.  M.  F.  of  the  disc  is 
equal  to  the  product  of  the  intensity  in  which  it  runs,  the 
number  of  revolutions  it  makes  per  second,  and  its  active  sur- 
face in  square  centimetres.  To  reduce  this  E.  M.  F.  to  volts, 
we  have  to  divide  by  100,000,000. 

284.  There  are  two  recognized  types  of  commutatorless 
continuous-current  dynamos;  namely,  the  disc  type  and  the 
cylinder  type.  The  outlines  of  a  particular  form  of  the  disc  type 
are  represented  in  Fig.  187.  Here  the  shaft  S  S,  usually  hori- 


CONTINUOUS-CURRENT  GENERATORS. 


237 


zontal,  carries  a  concentric,  perpendicular  disc  of  copper  or 
iron,  rotating  in  a  vertical  plane,  in  the  ring-shaped  magnetic 
frame,  in  a  circular  groove,  through  the  flux  produced  by  two 
coils  of  wire.  The  general  direction  of  the  magnetic  flux, 
through  the  field  frame  and  disc,  is  represented  by  the  curved 
arrows.  It  will  be  observed  that  the  magnetic  flux  will  be 
uniformly  distributed  so  as  to  pass  through  the  rotating  disc 
at  right  angles.  Brushes  rest  on  the  periphery,  and  on  the 
shaft,  of  the  disc.  Inasmuch  as  the  E.  M.  F.  in  the  disc  is 
radially  directed  at  all  points,  the  brushes  for  carrying  off  the 
current  may  be  as  numerous  as  is  desired.  These  brushes  are 


FIG.   187.  —  DISC   TYPE   OF   COMMUTATORLESS   DIRECT-CURRENT    GENERATOR. 

marked  b,  b,  in  the  figure.     A  and  B,  are  the  main  terminals 
-of  the  machine,  and/,  /',  the  field  terminals. 

285.  If  we  suppose  that  the  intensity  &,  is  12,000  gausses, 
that  the  radius  of  the  disc  is  i  foot,  or  30.48  centimetres,  that 
the  active  surface  on  each  side  of  the  disc  is  2,500  square  cen- 
timetres, and  that  the  speed  of  rotation  is  2,400  revolutions  per 
minute,  or  40  revolutions  per  second,  then  the  E.  M.  F.  obtain- 
able from  the  machine  will  be  : 


2,500 


X 


100,000,000 

In  order  to  produce  an  E.  M.  F.  of  say  140  volts,   such  as 
would  be  required  for  continuous-current  central-station  gen- 


238  ELECTRO-DYNAMIC  MACHINERY. 

erators,  it  would  be  necessary  either  to  connect  a  number  of 
such  machines  in  series,  or  to  increase  the  diameter  of  the  disc, 
or  to  increase  the  speed  of  rotation.  It  would,  probably,  be 
unsafe  to  run  the  disc  at  a  peripheral  speed  exceeding  200  miles 
per  hour,  owing  to  the  dangerously  powerful  mechanical 
stresses  that  would  be  developed  in  it  by  centrifugal  force. 
This  important  mechanical  consideration  imposes  a  limit  of 
speed  of  rotation  and  diameter  of  the  disc,  taken  conjointly. 
By  increasing,  however,  the  active  surface  of  the  disc,  and,  at 
the  same  time,  working  at  a  safe  peripheral  velocity,  it  would 


FIG.   l88. — DIAGRAM    SHOWING   FLUX    DENSITY    THROUGH    DISC   ALONG 
A    RADIUS. 

be  possible  to  construct  large  disc  generators  of  this  type  for 
an  E.  M.  F.  of  100  or  150  volts. 

286.  It  should  be  borne  in  mind  that  although  such  machines- 
would  be  capable  of  producing  continuous  currents  without  the 
use  of  a  commutator,  yet  the  necessity  of  maintaining  efficient 
rubbing  contacts  on  the  periphery  of  the  rapidly-revolving  disc 
introduces  a  difficulty  and  waste  of  power  which  has  hitherto 
prevented  the  development  of   this    system,    and,    probably, 
accounts  for  the  fact  that  large  machines  of  this  type  do  not 
exist. 

287.  Irregularities  in  the  distribution  of  magnetic  flux  over 
the  surface  of  the  disc  may  give  rise  to  strong  eddy  currents 
and  waste  of  power  in  the  same.     If  the  flux  be  variable  along 
any  radius  of  the  disc  O  B,  as  represented  in  Fig.  188,  so  that 
the  intensity  (B,  is  no't  uniform  along  these  lines,  this  irregu- 
larity will  not  produce  eddy  currents  in  the  disc  unless  the  dis- 
tribution is  different  along  different  radii.     In  other  words,  if 


CONTINUOUS-CURRENT  GENERA  TORS. 


239 


the  distribution  of  magnetic  flux  and  intensity  are  symmetrical 
about  the  axis  of  rotation  of  the  disc,  the  irregularities  which 
exist  will  only  alter  the  intensity  of  E.  M.  F.  in  different 
elements  of  a  radius.  In  Fig.  188,  the  intensity,  instead  of 
being  uniform  from  centre  to  edge,  as  indicated  by  the  straight 
line  da  c,  increases  toward  the  edge,  following  the  line  o  a  b. 


FIG.   189. — CYLINDER   TYPE   OF    COMMUTATORLESS    CONTINUOUS-CURRENT 

GENERATOR. 

The  formula  for  determining  the  E.  M.  F.  of  the  disc  is  in 
such  case  rendered  somewhat  more  complex. 

288.  If,  however,  the  curve  o  a  b,  of  flux  intensity  along 
different  radii  is  different,  so  that  the  distribution  of  magnetic 
intensity  is  not  symmetrical  about  the  axis  of  rotation,  then 
eddy  currents  will  tend  to  form,  the  amount  of  power  so 
wasted  depending  upon  the  amount  of  irregularity,  the  resis- 
tivity of  the  material  in  the  disc,  and  the  load  on  the  machine. 


FIG.   190. — INDICATING   DIRECTION   OF    E.  M.  F.  INDUCED   IN   REVOLVING 

CYLINDER. 

289.  Fig.  189  represents  the  outlines  of  a  particular  form  of 
the  second,  or  cylindrical  type  of  commutatorless  continuous- 
current  generator.  Here  a  metallic  conducting  cylinder  cccc, 
revolves  concentrically  upon  the  shaft  S  S,  through  the  uniform 
magnetic  flux,  produced  by  the  field  frame  surrounding  it. 
Here,  however,  two  sets  of  brushes  bb,  b'b ',  have  to  be  applied 
to  the  edges  of  the  cylinder  in  order  to  supply  the  main  ter- 


Xl*       OFTHE 

MBNIVERSIT 

^S 


2 40  ELECTRO-DYNAMIC  MACHINERY. 

minals  A  and  B.     The  terminals  of  the  four  circular  coils  con- 
stituting the  field  winding  are  shown  at/,  /'. 

290.  If  the  magnetic  intensity  produced  by  the  field  is 
uniform,  the  E.  M.  F.  will  be  generated  in  lines  along  the  sur- 
face of  the  cylinder  parallel  to  its  axis,  as  represented  in  Fig. 
190.  If  v,  be  the  peripheral  velocity  of  the  cylinder  in  centi- 
metres per  second,  /,  the  length  of  the  cylinder  in  centimetres, 
and  (R  the  uniform  intensity,  in  gausses,  the  E.  M.  F.  generated 
by  the  machine  will  be: 

v  /(B 

e  = volts. 

100,000,000 

Machines  of  the  cylindrical  type  have  been  constructed  and 
used  for  electrolytic  apparatus,  and  give  very  powerful  cur- 
rents, as  compared  with  ordinary  generators  of  the  same 
dimensions  employing  commutators.  Unsatisfactory  as  these 
unipolar  machines  have  so  far  proved,  except  in  special  cases, 
they  are,  nevertheless,  the  only  dynamos  which  have  yet  been 
successfully  constructed  for  furnishing  continuous  currents 
without  the  use  of  a  commutator. 


CHAPTER  XXIV. 

ELECTRO-DYNAMIC    FORCE. 

291.  In  discussing  the  magnetic  flux  surrounding  an  active 
conductor,  we  have  observed  in  Par.  34,  that  it  is  distributed 
in  concentric  cylinders  around  the  conductor,  as  shown  in 
Figs.  27  and  28.  It  is  evident  that  if  a  straight  conducting 


FIG.  igi. — STRAIGHT   CONDUCTOR   IN    UNIFORM   MAGNETIC   FLUX. 

wire  A  B,  say  /  cms.  in  length,  as  shown  in  Fig.  191,  be  situated 
in  the  uniform  magnetic  flux  represented  by  the  arrows,  the 
flux  will  exert  no  mechanical  influence  upon  the  wire.  If,  how- 
ever, the  wire  carries  a  uniform  current  in  the  direction  from 


t 


FIG.    192. — MAGNETIC  FLUX   SURROUNDING  ACTIVE  CONDUCTOR. 

A  to  B,  then,  as  is  represented  diagrammatically  in  Fig.  192, 
the  system  of  concentric  circular  flux,  indicated  by  a  single 
circle  of  arrows,  will  be  established  around  the  wire,  appearing 
clockwise  to  an  observer  looking  from  A,  along  the  direction 
in  which  the  current  flows,  and,  as  has  already  been  pointed 
out,  this  circular  magnetic  flux  will  have  an  intensity  propor- 
tional to  the  current  strength. 

241 


242 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


292.  If  such  a  conductor  be  introduced  into  a  uniform  mag- 
netic flux,  as  is  represented  in  Fig.  193,  it  is  evident  that  above 
the  wire  at  C,  the  direction  of  the  flux  produced  by  the  current 
is  the  same  as  that  of  the  field,  while  below  the  wire  at  Dy  the 
direction  of  the  flux  from  the  current  is  opposite  to  that  from 
the  field.  Consequently,  the  flux  above  the  wire  is  denser, 


FIG.   193. — DIAGRAM    SHOWING   DIRECTION    IN   ELECTRO-DYNAMIC   FORCE. 

and  that  below  the  wire  is  weaker,  or  less  dense,  than  that  of 
the  rest  of  the  field.  The  effect  of  this  dissymmetrical  distri- 
bution of  the  flux  density  in  the  immediate  neighborhood  of 
the  wire,  is  to  produce  a  mechanical  force  exerted  upon  the 
substance  of  the  wire,  called  the  electro-dynamic  force,  tending 
to  move  it  from  the  region  of  densest  flux  toward  the  region 
of  weakest  flux;  or,  in  the  case  of  Fig.  193,  vertically  down- 


FIG.  194. — DIAGRAM   SHOWING   DIRECTION   IN   ELECTRO-DYNAMIC   FORCE. 

ward,  as  indicated  by  the  large  arrow.  If,  however,  the  direc- 
tion of  the  current  in  the  wire  be  reversed,  as  shown  in  Fig. 
194,  and  that  of  the  external  field  remain  unchanged,  the  flux 
will  be  densest  beneath  the  wire  and  weakest  above  it,  so  that 
the  electro-dynamic  force  will  now  be  exerted  in  the  opposite 
direction,  or  vertically  upward,  as  shown  by  the  large  arrows. 


ELECTRO-DYNAMIC  FORCE.  243 

293.  If  the  direction  both  of  the  current  in  the  wire  and  the 
flux    in  the  external  field  be   reversed,  the   direction  of   the 
electro-dynamic  force  will  not  be  changed,  as  is  represented  in 
Fig.  195,  where  the  direction  of  the  electro-dynamic  force  is 
downward  as  in   Fig.  193,  though  the  direction  of  the  current 
and  the  direction  of  the  magnetic  field  are  both  reversed. 

294.  A   convenient  rule  for  remembering  the  direction  of 
the  motion  is   known  as   Fleming's  hand  rule.     It   is,  in  gen- 
eral, the  same  as  that  already  given  for  dynamos  in  Par.  81, 
except  that  in  applying  it,  the  left  hand  must  be  used  instead 
of  the  right.     For  example,  if  the  hand  be  held  as  in  the  rule 
for  dynamos,  if  the/orefinger  of  the  left  hand  shows  the  direc- 
tion of  the/" lux,  and  the  middle  finger  the  direction  of  the  cur- 


FIG.  195. — DIAGRAM     SHOWING    DIRECTION    IN   ELECTRO-DYNAMIC   FORCE. 

rent,  then  the  thumb  will  show  the  direction  of  the  motion. 
It  must  be  remembered,  that  in  applying  Fleming's  rule,  the 
right  hand  is  used  for  dynamos  in  determining  the  direction  of 
the  induced  E.  M.  F.,  and  the  left  hand  for  motors  in  deter- 
mining the  direction  of  motion. 

295.  We  shall  now  determine  the  value  of  the  electro- 
dynamic  force  in  any  given  case,  on  the  doctrine  of  the  con- 
servation of  energy.  To  do  this,  we  may  consider  the  ideal 
apparatus,  represented  in  Fig.  196,  where  a  horizontal  con- 
ductor E  F,  moves  without  friction  against  two  vertical  metallic 
uprights  A  B,  and  CD.  This  conductor  is  supported  by  a 
weightless  thread,  passing  over  two  frictionless  pulleys  P,  P, 
and  bearing  a  weight  W.  If  now  a  current  enters  the  upright 
A  B,  and,  passing  through  the  sliding  conductor  E  Fy  leaves  the 


244 


ELECTRO-D  YNA MIC  MA  CHINER  Y. 


upright  CD,  at  C,  then,  in  accordance  with  the  preceding 
principles,  under  the  influence  of  the  uniform  magnetic  flux 
passing  horizontally  across  the  bar  in  the  direction  of  the 
arrows,  an  electro-dynamic  force  will  act  vertically  downwards 
upon  the  rod.  If  this  electro-dynamic  force  is  sufficiently 
powerful  to  raise  the  weight  W,  it  will  evidently  do  work  on 
such  weight,  as  soon  as  it  causes  the  bar  to  move.  Let  us 
suppose  that  it  produces  a  steady  velocity  of  the  bar  E  F,  of  v 
cms.  per  second,  in  a  downward  direction.  Then  if  /,  be  the 


FIG.   196. — IDEAL   ELECTRO-DYNAMIC   MOTOR. 

electro-dynamic  force  in  dynes  exerted  on  the  bar,  the  activity 
exerted  will  be,  v  f  centimetre-dynes-per-second,  or  ergs-per- 
second.  Since  10,000,000  ergs  make  one  joule,  this  will  be  an 
activity  of 

vf 


10,000,000 


joules-per-second,  or  watts. 


This  activity  will  be  expended  in  raising  the  weight  W, 
assuming  the  absence  of  friction.  As  in  all  cases  of  work 
expended,  the  requisite  activity  to  perform  such  work  must  be 
drawn  from  some  source,  and  in  this  case  the  source  is  the 
electric  circuit. 

296.  When  the  bar  of  length  /  cms.  moves  with  the  velocity 
of  v  centimetres-per-second,  through  the  uniform  flux  of  den- 


ELECTRO-DYNAMIC  FORCE.  245 

sity  (&,  it  must  generate  an  E.  M.  F.  as  stated  in  Par.  82,  of 
e  —  (&  /  vt  C.  G.  S.  units,  or 

&/v 

volts. 

100,000,000 

This  E.  M.  F.  is  always  directed  against  the  current  in  the 
wire,  and  is,  therefore,  always  a  C.  E.  M.  F.  in  the  circuit. 
The  current  of  /  amperes  passing  through  the  rod  will,  there- 
fore, do  work  upon  this  C.  E.  M.  F.  with  an  activity  of 

e  i  watts  —  -  /  watts. 

100,000,000 

This  activity  must  be  equal  to  the  activity  exerted  mechan- 
ically by  the  system,  so  that  we  have  the  equation, 

vf  (B  Iv  i 

10,000,000        100,000,000 
From  which, 

.       <B  // 

/  =   -  dynes. 

10 

—  will  be  the  number  of  C.  G.  S.  units  of  current,  since  the 
10 

C.  G.  S.  unit  of  current  is  10  amperes,  so  that  the  funda- 
mental expression  for  the  electro-dynamic  force  exerted  on  a 
straight  wire,  lying  or  moving  at  right  angles  across  a  uni- 
form flux,  is 

/=(&//  dynes, 

where  /,  is  expressed  in  C.  G.  S.  units  of  current.  Since  the 
force  of  981  dynes  is,  approximately,  the  force  exerted  by 
gravity  upon  one  gramme,  we  have 

/  = or grammes  weight, 

981         9,810 

and  since  453.6  grammes  make  one  pound,/,  expressed  in 
pounds  weight  will  be 

/r>    7  / 

/  — — -  pounds  weight. 

"  10  x  981  X  453-6 

If,  for  example,  the  rod  shown  in  Fig.  196  had  a  length  of 
one  metre,  or  100  centimetres,  and  moved  in  the  earth's  flux 
whose  horizontal  component  =  0.2  gauss,  then  if  supplied 
with  a  uniform  current  of  1,000  amperes,  it  would  exert  a 

downward  force  of  0.2  x  100  X  — =  2,000  dynes;  or  ap- 

10 

proximately,  2  grammes  weight. 


246  ELECTRO-DYNAMIC  MACHINERY. 

297.  We  have  heretofore  considered   the  wire   as   lying  at 
right  angles  to  the  flux  through  which  it  is  moved.     If,  how- 
ever, the  wire  A  B,  lies  obliquely  to  the  flux,  at  an  angle  ft,  as 
is  represented  in  Fig.  197,  then  the  effective  length  of  the  wire, 
or  the  projected  length  of  AB,  at  right  angles  to  the  flux  will 
be  a  b.      In   symbols   this  will   be   /  sin  /?,  and   the   electro- 
dynamic  force  will  be 

/  =  &  /  sin  /3  —  dynes. 

298.  Although  such    a  machine  as  is    represented   in   Fig. 
196  is  capable  of  performing  mechanical  work,  and  might  be, 
therefore,  regarded  as  a  form  of  electro -dynamic  motor,  yet  all 


FIG.    197. — WIRE    LYING    OBLIQUE   TO    MAGNETIC   FLUX. 

practical  electro-dynamic  motors  are  operated  by  means  of 
conducting  loops,  capable  of  rotating  about  an  axis.  We 
shall,  therefore,  now  consider  such  forms  of  conductor. 

299.  If  the  rectangular  loop  a  a"  a'"  a"",  Fig.  198,  placed  in  a 
horizontal  plane,  in  a  uniform  magnetic  flux,  be  capable  of 
rotation  about  the  axis  oo,  then  if  a  current  of  i  amperes  be 
caused  to  flow  through  the  loop  in  the  direction  a'  a"  a'"  a"", 
electro-dynamic  forces  will  be  set  up,  according  to  the  preced- 
ing principles,  upon  the  sides  a'  a",  and  a'"  a"",  but  there  will 
be  no  electro-dynamic  force  upon  the  remaining  two  sides. 
Under  the  influence  of  these  electro-dynamic  forces,  the  side 
a'  a",  will  tend  to  move  upwards,  and  the  side  a'"  a"",  down- 
wards. The  loop,  therefore,  if  free  to  move,  will  rotate,  and 
will  occupy  the  successive  positions  £,  c  and  d.  At  the  last 
named  position,  the  plane  of  the  loop  being  vertical,  although 
the  electro-dynamic  force  will  still  exist,  tending  to  move  the 
the  side  a'  a",  downwards,  and  the  side  a'"  a"",  upwards,  yet 


ELECTRO-DYNAMIC  FORCE.  247 

these  forces  can  produce  no  motion,  being  in  opposite  direc- 
tions and  in  the  same  plane  as  the  axis;  or,  in  other  words, 
the  loop  considered  as  a  rotatable  system  is  at  a  dead  point. 

300.  It  is  clear,  from  what  has  been  already  explained,  that 
if  the  direction  of  the  current  in  the  loop  had  been  reversed 
while  the  direction  of  the  field  flux  remained  the  same  ;  or,  if 
the  direction  of  the  field  flux  be  reversed  with  the  direction  of 
current  remaining  the  same,  that  the  direction  of  the  electro- 
dynamic  forces  would  have  been  changed,  tending  to  move 
the  side  a1  a",  upwards  and  the  side  a'"  a"",  downwards,  so  that 
the  loop  would  have  rotated  in  the  opposite  direction  until  it 
reached  the  vertical  plane.  Consequently,  when  a  loop,  lying 


FIG.  198. — LOOP   OF   ACTIVE   CONDUCTOR   IN   MAGNETIC   FLUX. 

in  the  plane  of  the  magnetic  flux,  receives  an  electric  current 
it  tends  to  rotate,  and,  if  free,  will  rotate  until  it  stands  at 
right  angles  to  the  magnetic  flux. 

301.  An  inspection  of  the  figure  will  show  that  when  the 
loop  is  in  the  plane  of  magnetic  flux,  that  is  to  say,  when  the 
rotary  electro-dynamic  force  is  a  maximum,  the  loop  contains 
no  magnetic  flux  passing  through  it,  while  when  the  loop  is  in 
the  vertical  position,  and  the  rotary  power  of  the  electro- 
dynamic  force  is  zero,  it  has  the  maximum  amount  of  flux 
passing  through  it.  The  effect  of  the  electro-dynamic  force, 
therefore,  has  been  to  move  the  conducting  loop  out  of  the 
position  in  which  no  flux  passes  through  it,  into  the  position 
in  which  the  maximum  possible  amount  of  flux  passes  through 
it,  under  the  given  conditions. 


248 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


302.  When  an  active  conductor  is  bent  in  the  form  of  a  loopr 
such,  for  example,  as  is  shown  in  Fig.  199,  all  the  flux  pro- 
duced by  the  loop  will  thread  or  pass  through  the  loop  in  the 
same  direction,  and  this  direction  will  depend  upon  the  direc- 
tion of  the  current  around  the  loop.  If,  for  example,  we  con- 
sider the  loop  a1  a"2  a3  a\  independently  of  the  magnetic  flux 
into  which  it  is  introduced,  and  send  a  current  of  /  amperes,  in 
the  same  direction  as  before  around  the  loop,  the  general  dis- 
tribution of  the  flux  around  the  sides  of  the  loop  is  represented 


FIG.    199. — DIAGRAM    SHOWING   COINCIDENCE    IN    DIRECTION   OF   FLUX   PATHS 
AROUND    A   LOOP   OF   ACTIVE    CONDUCTOR. 


by  the  circular  arrows,  from  which  it  will  be  seen  that  all  the 
flux  passes  downward  through  the  loop  as  represented  by  the 
large  arrow.  If  this  loop  be  now  introduced  into  the  external 
magnetic  flux,  as  shown  in  Fig.  192,  it  will  tend  to  rotate,  until 
the  external  magnetic  flux  passes  through  it  in  the  same  direc- 
tion as  the  flux  produced  by  its  own  current.  Generally, 
therefore,  it  may  be  stated  that  when  an  active  conducting 
loop  is  brought  into  a  magnetic  field,  the  electro-dynamic 
force  tends  to  move  the  loop  until  its  flux  coincides  in  direc- 
tion with  that  of  the  field. 

303.  During  the  rotation  of  the  loop  as  shown  in  Fig.  198 
from  the  position  a,  to  the  position  d,  the  loop  will  embrace 
a  certain  amount  of  flux,  say  0  webers,  from  the  external 
field.  In  other  words,  in  the  position  d,  the  loop  holds  $ 
webers  more  flux  than  in  the  position  a.  If  the  current  / 
amperes,  passing  through  the  loop  be  uniform  during  the 


ELECTRO-DYNAMIC  FORCE.  249 

rotation,  then  it  can  readily  be  shown  that  the  amount  of 
work  performed  by  the  loop  during  this  motion  is, 

„,       *  # 

W  :=  —  ergs, 

but  this  motion  comprises  only  one  quarter  of  a  complete 
revolution.  At  the  same  rate  the  work  done  in  one  revolu- 
tion would  be, 

4  *  $  4  /  $ 

ergs  —  -  ioules. 

10  10  x    10,000,000 

304.  In  a  bipolar  motor  with  a  drum-wound  armature  on 
which  there  are  w  wires,  counted  once  completely  around  the 

periphery,  or  —  loops  over  the  surface,  there  will  be  ~-  times 

as  much  work  performed  in  one  revolution  as  though  a  single 
loop  existed  on  the  surface;  the  work-per-revolution  will, 
therefore,  be 

4  /  $        w 

—  joules. 

100, 000,OOO '2 

If  now  the  motor  makes  n  revolutions  per  second,  the  work 
performed  will  be  n  times  this  number  of  joules  in  a  second,  or 

4  /  £>  n        w  2  i  $  n  w 

watts.  = watts. 


100,000,000  *2  100,000,000 

Then,  as  will  be  shown  hereafter,  the  current  supplied  at  the 
brushes  of  the  motor  will  be  /  =  2  i  amperes,  if  /,  be  the  cur- 
rent through  each  loop,  so  that  the  activity  absorbed  by  the 
motor  will  be, 

/  $  n  w 

watts. 

100,000,000 

We  know  that  the  E.  M.  F.  of  a  rotating  armature  is 

^)   72   2£/ 

e  = volts  (see  par.  132), 

100,000,000 

so  that  we  have  simply,  that  the  activity  absorbed  by  the 
motor  armature  available  for  mechanical  work  is  e  I  watts,  and 
this  must  be  true  under  all  conditions,  in  every  motor. 

When  an  E.  M.  F.  of  E  volts  acts  in  the  same  direction  as  a 
current  7  amperes;  /.  e.,  drives  the  current,  it  does  work  on 
the  current  with  an  activity  of  E  I  watts,  the  activity  being 
expended  by  the  source  of  E.  M.  F.  On  the  other  hand, 
when  an  E.  M.  F.  of  E  volts  acts  in  the  opposite  direction  to 


250  ELECTRO-DYNAMIC  MACHINERY. 

a  current  of  /  amperes,  and  therefore  opposes  it,  or  is  a 
C.  E.  M.  F.  to  the  current,  the  current  does  work  on  the 
C.  E.  M.  F.  with  an  activity  of  E  I  watts,  and  this  activity 
appears  at  the  source  of  C.  E.  M.  F.  If  the  C.  E.  M.  F.  be 
merely  apparent  in  a  conductor  containing  a  resistance  R 
ohms,  as  a  drop  I R  volts,  the  activity  E  I  —  I*  R,  and  is 
expended  in  the  resistance  as  heat.  If  the  C.  E.  M.  F.  be 
caused  by  electro-magnetic  induction,  as  in  a  revolving  motor 
armature,  the  activity  E  /,  is  expended  in  mechanical  work, 
including  frictions  of  every  kind. 


CHAPTER  XXV. 

MOTOR    TORQUE. 

305.  We  now  proceed  to  determine  the  values  of  the  rotary 
effort  of  a  loop  at  different  positions  around  the  axis.  This 
rotary  effort  is  called  the  torque.  Torque  may  be  defined  as 
the  moment  of  a  force  about  an  axis  of  rotation.  The  torque 
is  measured  by  the  product  of  a  force  and  the  radius  at  which 
it  acts.  Thus,  if  in  Fig.  200,  a  weight  of  /*,  pounds,  be  sus- 
pended from  the  pulley  F,  and,  therefore,  acts  at  a  radius  / 
feet,  the  torque  exerted  by  the  weight  about  the  axis  will  be 
P  I  pounds-feet.  If  JP,  be  expressed  in  grammes,  and  /,  in 
centimetres,  the  torque  will  be  expressed  in  gramme-centi- 
metres; and  if  P,  be  in  dynes  and  /,  in  centimetres,  the  torque 


100  LB& 
FIG.    200. — DIAGRAM   ILLUSTRATING   NATURE   AND    AMOUNT   OF   TORQUE. 

will  be  expressed  in  dyne-centimetres.  Thus,  at  A,  Fig.  200, 
the  torque  about  the  axis  of  the  pulley  Y,  is  400  pounds-feet. 
At  B,  it  is  800  pounds-feet.  At  Cy  it  is  400  pounds-feet. 

As  an  example  of  the  practical  application  of  torque  in 
electric  motors,  let  us  suppose  that  the  pulley  JP9  is  attached 
to  the  armature  shaft  of  a  motor,  and  that  the  motor  succeeds 
in  raising  the  weight  J/",  by  the  cord  over  the  periphery  of 
the  pulley,  then  the  motor  will  exert  a  torque  at  the  pulley 
of  M  I  pounds-feet.  Thus,  if  the  pulley  be  12  inches  in 
diameter  =  0.5  foot  in  radius,  and  the  weight  be  100  pounds, 
then  if  the  thickness  of  the  cord  be  neglected,  the  torque 

251 


252  ELECTRO-DYNAMIC  MACHINERY. 

exerted   by  the    motor   will   be    100    x  0.5  =  50  pounds-feet, 
about  the  shaft,  at  the  pulley. 

306.  The  work  done  by  the  torque  which  produces  rotation 
through  an  angle  /?,  expressed  in  radians,  is  the  product  of  the 
torque  and  the  angle.     Thus,  if  the  torque  r,  rotates  the  sys- 
tem  through   unit  angle   about  an  axis,    the   torque  does  an 
amount  of  work  =  r.     If  the  torque  be  expressed  in  pounds- 
feet,  this  amount  of  work  will  be  in  foot-pounds.      If  the  torque 
be  expressed  in  gm.-cms.,  the  work  will  be  expressed  in  cm.- 
gms.,  and  finally,  if  the  torque  be  expressed  in  dyne-cms,  the 
work  will  be  expressed  in  cm. -dynes,  or  ergs.     Since  there  are 
2  7t  radians  in  one  complete  revolution,  the  amount  of  work  done 
by  a  torque  r,  in  one  complete  revolution  will  be  2  n  r  units 
of  work.     For  example,  the  motor  in  the  last  paragraph,  which 
produced  a  torque  of  50  pounds-feet,  would,  in  one  revolution, 
do  an  amount  of  work  represented  by  50  X  2  TT  =  314. 16  foot- 
pounds.    It  is   evident,   in   fact,   that  since    the    diameter   of 
the  pulley  is  one  foot,  one  complete  revolution  will    lift  the 
weight  M,  through  3.1416  feet,  and  the  work  done  in  raising 
a  loo-pound  weight  through  this  distance  will  be  314.16  foot- 
pounds.    Similarly,  if  &?,  expressed  in  radians  per  second,  be 
the  angular  velocity  produced  by  the  torque,  then  the  activity 
of  this  torque  will  be  r  GO  units  of  work  per    second.     For 
example,  a  motor  making  1,200  revolutions  per  minute,  or  20 
revolutions  per  second,  has  an  angular  velocity  of  20    x    27T  = 
125.7  radians  per  second.     If  the  torque  of  this  motor  be  10,000 
dyne-cms.,  the  activity  of  this  torque;  /.  ^.,  of  the  motor,  will 
be  10,000  X  125.7  =  1,257,000  ergs  per  second*  =  0.1257  watt. 

307.  A  torque  must  necessarily  be  independent  of  the  radius 
at  which  it  is  measured.     Thus,  if  a  motor  shaft  is  capable  of 
lifting  a  pound  weight  at  a  radius  of  one  foot;  /.  e.,  of  exerting 
a  torque  of  one  pound-foot,  then  it  will  evidently  be  capable 
of  supporting  half  a  pound  at  a  radius  of  two  feet,  or  one  third 
of  a  pound  at  a  radius  of  three  feet,  etc.     In  each  case  the 
torque  will  be  the  same;  /.  e.,  one  pound-foot. 

308.  The  torque  produced  by  a  loop,  situated  in  a  uniform 
magnetic  flux,  varies  with  the  angular  position  of  the  loop. 


MOTOR    TORQUE.  253 

For  example,  returning  to  Fig.  198,  the  torque  of  the  active 
loop  is  zero  in  the  position  dy  and  is  a  maximum  in  the 
position  a.  The  electro-dynamic  force  exerted  by  the  side  a'  a" 

will  be  (B  /  —  dynes,  and,    if  the   radius  at   which   this  acts 
10 

about  the  axis — /.  ^.,  half  the  length  of  the  side  a'  a"",  be  a 
cms.,  then  torque  exerted  by  this  side  will  be  -  -  dyne-cms. 

Similarly,  the  torque  exerted  in  the  same  direction  around  the 


FIG.    201. — DIAGRAM    SHOWING    SMALL    ANGULAR   DISPLACEMENT   ABOUT   ITS 
AXIS,    OF   A   LOOP   IN    UNIFORM   MAGNETIC   FLUX    IN    ITS   PLANE. 

axis  by  the  side  a'"  a'",  will  be  also —  dyne-cms.,  so  that 

2  ($>  1 1  a 
the  total  torque  around  the  axis  will  be  dyne-cms. 

If  the  loop  moves  under  the  influence  of  this  torque  through  a 

very  small  angle  dp,  the  work  done  will  be  i:  d  ft  = '•    -  dp, 

but  a  d  fi  =  ds,   the  small  arc  moved  through,   as  shown  in 

Fie:.   201,   so  that  the   work   done  will  be    — .     The 

10 

amount  of  flux  linked  with  the  loop  during  this  small  movement 
will  be  2  (B  ds  I  =  d  <£,  so  that  the  work  done  becomes  —  d  #, 

or  I  d  0  where  I,  stands  for  the  current  strength  in  C.  G.  S. 
units  of  ten  amperes  each.  Consequently,  in  any  small  excur- 
sion of  the  loop,  the  work  done  will  always  be  the  product  of 


254 


ELECTRO-DYNAMIC  MACHINERY. 


the  current  strength  and  the  increase  of  flux  therewith 
enclosed.  It  is  evident  that  the  amount  of  flux  which  is 
brought  within  the  loop  by  a  given  small  excursion,  varies 
with  the  position  of  the  loop;  that  is  to  say,  a  small  excursion 
through  the  arc  ds,  at  the  position  represented  both  in  plane 
and  isometric  projection,  where  the  plane  of  the  loop  coin- 
cides with  the  direction  of  the  flux,  in  Fig.  201,  will  introduce 
an  amount  of  flux  =  /  (B  ds.  But  the  same  small  excursion  in 


FIG.    202. — SMALL   ANGULAR    DISPLACEMENT   OF   A   LOOP   IN   UNIFORM    MAG- 
NETIC  FLUX    PERPENDICULAR   TO    ITS    PLANE. 

the  position  represented  in  Fig.  202 — /.  ^.,  where  the  plane 
of  the  loop  is  perpendicular  to  the  flux — will  introduce  practi- 
cally no  additional  flux  into  the  loop.  At  any  intermediate 
position,  it  will  be  evident  that  the  flux  introduced  by  a  small 
excursion  of  arc  ds,  will  be  /  ds  ($>  cos  /?,  where  /?,  is  the  angle 
included  between  the  plane  of  the  loop  and  the  direction 
of  magnetic  flux.  The  torque  exerted  by  the  loop,  therefore, 
varies  as  the  cosine  of  the  angle  between  the  plane  of  the  loop 
and  the  direction  of  the  external  flux. 

309.  Let  us  now  consider  the  application  of  the  foregoing 
principles  to  the  simplest  form  of  electro-magnetic  motor.  For 
this  purpose  we  will  consider  a  smooth-core  armature  A,  Fig. 
203,  situated  in  a  bipolar  field.  We  will  suppose  that  the  total 
magnetic  flux  passing  through  the  loop  of  the  wire  in  the 
position  shown,  from  the  north  pole  N,  to  the  south  pole  S,  is 
$  webers,  and  that  a  steady  current  of*  amperes,  is  maintained 
through  the  loop  of  wire  attached  to  the  armature  core.  In 
the  position  of  the  loop  as  shown  in  Fig.  203,  there  will  be  no- 


MOTOR    TORQUE.  255 

rotary  electro-dynamic  force  exerted  upon  the  wire,  and  the 
armature  will  be  at  a  dead  point.  If,  however,  the  armature 
be  moved  from  this  position  into  that  shown  in  Fig.  204,  so 
that  it  enters  the  magnetic  flux,  assumed  to  be  uniformly  dis- 
tributed over  the  surface  of  the  poles  and  armature  core,  then 
a  rotary  electro-dynamic  force  is  set  up  on  the  wire,  and  com- 


FIG.  2O3. — DRUM  ARMATURE  WITH  SINGLE  TURN  OF  ACTIVE  CONDUCTORS 
AT  DEAD  POINT. 

municated  from  the  wire  to  the  armature  core  on  which  it  is 

/      d  4> 
secured.      The  torque  being — .  dyne-cms.,  where/,  is  the 

d  3> 

current  strength  in  amperes,  and  — -  the  rate  at  which  flux  en- 
closed by  the  loop  is  altered  per  unit  angle  of  displacement. 
If,  for  example,  the  total  flux  $  =  i  megaweber,  and  the  polar 


FIG.    204. — ACTIVE   CONDUCTOR   ENTERING  POLAR   FLUX. 

angle  over  which  we  assume  that  this  flux  is  uniformly  dis- 
tributed is  120°,  or  =  —  radians,  then  the  rate  of  emptying 
flux  from  the  loop  during  its  passage  through  the  polar  arc  will 
be  -  -  =  — — 9- —  webers-per-radian,  and  if  the  strength 

T 

of  current  in  the  loop  be  maintained  at  20  amperes,  the  torque 
exerted  by  the  electro-dynamic  forces  around  the  armature  shaft 

20       1,500,000 
will  be  —  X  -  -  =  955,000  dyne-cms.     Since  a  torque 

TO  7t 


256  ELECTRO-DYNAMIC  MACHINERY, 

of  i  pound-foot  =  13,550,000  dyne-cms.,  this  torque  would  be 

represented  by  =  0.0705     pound-foot,    or    0.0705 

i3,55°>000 
pound  at  one  foot  radius. 

The  armature  will  continue  to  move   under  this  torque,  if 
free  to  do  so,  until  the  position  of  Fig.   205  is  reached,  where 


FIG.  205. — ACTIVE  CONDUCTOR  LEAVING  POLAR  FLUX. 

it  is  evident  that  a  still  further  displacement  will  not  increase 
the  amount  of  flux  threaded  through  the  loop. 

The  amount  of  work  which  will  have  been  performed  by  the 
electro-dynamic  forces  during  this  angular  displacement  of  120° 

or  -  —  radians,  will  have  been  t  ft  —  955,000  X =  2,000,000 

o  «5 

/  20 

ergs,  or,  simply  —  $  = —  x  1,000,000  =  2,000,000  ergs  =  0.2 
joule. 

310.  The  armature  may  continue  by  its  momentum  to  move 
past  the  position  of  Fig.  205,  to  that  of  Fig.  206.    As  soon  as  it 


FIG.    206. — ACTIVE    CONDUCTOR   RE-ENTERING    POLAR   FLUX,    AND    ACTED    ON 
BY   OPPOSING   ELECTRO-DYNAMIC   FORCE. 

reaches  the  latter  position,  a  counter  electro-dynamic  force  will 
be  exerted  upon  it,  tending  to  arrest  and  reverse  its  motion. 
Consequently,  if  the  electro-dynamic  force  is  to  produce  a  con- 
tinuous rotation,  it  is  necessary  that  the  direction  of  the  cur- 
rent through  the  coil  be  reversed  at  this  point;  /.  ^.,  commuted, 
or  the  direction  of  the  field  be  reversed  as  soon  as  this  point  is 


MOTOR    TORQUE.  257 

reached.  As  it  is  not  usually  practicable  to  reverse  the  field, 
the  direction  of  current  through  the  coil  is  reversed  by  means 
of  a  commutator,  so  that  when  the  position  of  Fig.  206  is 
reached,  the  current  is  passing  through  the  wire  in  the  opposite 
direction  to  that  as  shown  by  the  arrow.  Under  these  circum- 
stances, the  electro-dynamic  force  and  torque  continue  in  the 
same  direction  around  the  axis  of  the  armature  and  expend 
another  0.2  joule  upon  the  armature  in  its  rotation  to  the 
original  position  shown  in  Fig.  203. 

It  is  to  be  remembered  that  the  representation  of  the  flux  in 
Figs.  203-206  is  diagrammatic,  since  the  flux  in  the  entrefer  is 
rarely  uniform,  never  terminates  abruptly  at  the  polar*  edges, 
and  is,  moreover,  affected  by  the  flux  produced  around  the 
active  conductor. 

311.  The  total  amount  of  work  done  in  one  complete  revolu- 
.tion  of  the  armature  upon  a  single  turn  of  active  conductor  is, 

,  2  i  $  2   i  0 

therefore,  -  ergs,  or  -  joules. 

10  100,000,000 

If  the  load  on  the  motor  be  small,  so  that  the  momentum  of 
the  armature  can  be  depended  upon  to  carry  it  past  the  dead- 
points  which  occur  twice  in  each  complete  revolution,  the 
armature  will  make,  say  n,  revolutions  per  second,  and  the 
amount  of  work  absorbed  by  the  armature  loop  in  this  time 

n  i  $  n 

will  be  -    joules    in    a    second,   or  an    activity   of 
100,000,000    • 

2  *  $  n 

—  watts. 


100,000,000 

The  E.  M.  F.  generated  by  the  rotation  of  this  loop  through 


ft    tyy 

the  magnetic  field,  by  dynamo  action,  will  be  - 

100,000,000 

volts,  (Par.  132)  where  w,  in  this  case  is  2,  since  there  are  two 
conductors  upon  the  surface  of  the  armature,  counting  once 
completely  around.  The  C.  E.  M.  F.  will,  therefore,  be 

2  $  n 

volts,  and  the  activity  of  the  electric  current 
100,000,000 

upon  this  C.  E.  M.  F.  will  be  -         watts,  as   above. 

100,000,000 

Hence  it  appears  that  in  this,  as  in  every  case,  the  torque  and 
work  produced  by  an  electro-magnetic  motor  depends  upon 
the  C.  E.  M.  F.  it  can  exert  as  a  dynamo. 


258  ELECTRO-DYNAMIC  MACHINERY. 

312.  Fig.  207  represents  a  Gramme-ring  armature,  carrying 
a  single  turn  of  conductor,  situated  in  a  bipolar  field.  If  the 
total  useful  flux  through  the  armature  is  $  webers,  as  before, 

$ 
half  of  this  amount  will  pass  through  the  turn,  or  —  webers, 

since  the  flux  divides  itself  into  two  equal  portions,  as  repre- 
sented in  the  figure.  It  will  be  evident,  as  before,  that  start- 
ing at  the  position  of  Fig.  207,  there  will  be  no  rotary  electro- 
dynamic  force  exerted  upon  the  loop,  until  it  enters  the  flux, 


FIG.    2O7. — GRAMME-RING   ARMATURE   WITH    SINGLE   TURN   OF   ACTIVE   CON- 
DUCTOR   AT    DEAD    POINT. 

assumed  to  commence  beneath  the  edge  of  the  pole-piece,  and 

/       d  0 

the  torque  will  then  be  uniform  at  the  value  —    •  -— 7j        dyne- 

10     d  ft 

centimetres,  until  the  turn  emerges  from  beneath  the  pole-piece 

/      # 

at  Z.     The  work  done  in  this  passage  will  have  been    — «  .  — 

10      2 

ergs,  and  this  work  will  have  been  taken  from  the  circuit,  and,, 
therefore,  from  the  source  of  E.  M.  F.  driving  the  current  i, 
and  will  be  liberated  as  mechanical  work  (including  frictions). 
If,  by  the  aid  of  the  commutator,  the  direction  of  the  current 
around  the  loop  be  reversed,  the  turn,  when  caused,  either  by 
momentum  or  by  direct  displacement,  to  enter  the  field  at  £, 
Fig.  208,  will  again  receive  a  rotary  electro-dynamic  force 

whose  torque   is  —^- until  the  angle  /?,  has  been  again 

10     d  ft 

i     & 

passed,  when  the  work  performed  will  be  — *  ergs,  as  be- 
fore. The  total  work  done  upon  the  armature  in  one  revolu- 

/         ^        i  $ 
tion  will,  therefore,  be  '2  x  —  X  —  =  —   ergs,  and   if   the 

IO  2  IO 

armature  make  n  revolutions  per  second,  the  activity  expended 

/  0  n  i  $  n 

upon  it  will  be ergs  per  second  =  watts  •  but 

10  100,000,000 


MOTOR    TORQUE.  259 

considering  the   rotating  armature   in  this  case,  as  a  dynamo 

0  n 

armature,  its  E.  M.  F.   will  average  volts,    since 

100,000,000 

there    is   only    one    turn   of  the    wire    upon    its   surface,  and, 
consequently,    the   activity   expended    on  the   armature    will 

i.Q'n 

be  e  i  =  watts. 

100,000,000 

313.  We  have  hitherto  considered  that  the  armature,  whether 
of  the   Gramme-ring  or  drum   type,   possessed    only  a  single 


C  £' 

FIG.    208. — GRAMME-RING   ARMATURE   WITH   SINGLE   TURN   OF   ACTIVE   CON- 
DUCTOR. 

turn.  As  a  consequence  the  torque  exerted  by  a  constant  cur- 
rent in  the  armature  will  vary  between  a  certain  maximum  and 
zero,  that  is  to  say,  the  motor  will  possess  dead-points.  If, 
however,  a  number  of  turns  be  uniformly  wound  upon  the  arma- 
ture, as  in  the  dynamos  already  considered,  it  will  be  evident 
that  the  same  number  of  turns  will  always  be  situated  in  the 
magnetic  flux  beneath  the  poles  and  in  the  air  space  beyond 
them,  in  all  positions  of  the  armature,  and  that,  consequently, 
the  torque  exerted  upon  the  armature  will  be  constant  when 
the  magnetic  flux  and  the  current  strength  are  constant.  The 
torque  exerted  by  the  armature  with  w  wires  upon  its  surface, 

/    0  w 
counted   once  completely   around,  will  be       • —   dyne-cms., 

10    2  7t 

whether  for  a  Gramme-ring  or  a  drum  armature,  and  this 
whether  the  armature  be  smooth-core  or  toothed-core. 

That  this  is  the  case  will  be  evident  from  the  following  con- 
sideration.    The  work  done  on  a  single  wire  in  one  complete 

t  0 

revolution  is  —  ergs,  and  if  there  are  w  wires  on  the  surface 
10 

of  the  armature,  the  total  work  done  by  electro-dynamic  forces 

in  one  revolution  will  be  ergs.     But  the  work  done  by  a 

TO 


2  60  ELECTRO-D  YNA MIC  MA  CHINER  V. 

torque  T  dyne-cms,  exerted  through  an  angle  of  ft  radians  is 
r  fi  cm. -dynes  or  ergs,  and  since  one  revolution  is  2  n  radians, 
the  work  done  by  the  torque  will  be  2  n  T  ergs.  Therefore, 

2  n  t  =  ,  or  r  = — • dyne-cms. 

10  10  2   n 

For  example,  if  a  Gramme-ring  armature  has  200  turns  of 
wire,  counted  once  all  round  the  surface,  and  the  current 
strength  supplied  to  the  armature  from  the  external  circuit  to 
the  brushes  is  50  amperes,  while  the  total  useful  flux  passing 
from  one  pole  through  the  armature  across  to  the  other  pole  is 
5,000,000  wejpers,  or  5  megawebers,  then  the  torque  exerted  by 
the  armature  under  these  conditions  will  be, 

50       500,000,000  x  200  795,800,000 

—  x  - — —  =  795, 800,000  dyne-cms.  = 

10  *  27T  13,550,000 

pounds-feet  =  58.73  pounds-feet. 

314.  The  torque  produced  by  multipolar  continuous-current 
motors  is  independent  of  the  number  of  poles,  if  the  armature 
winding  be  of  the  multiple-connected  type ;  i.  e.,  if  there  are  as 
many  complete  circuits  through  the  armature  as  there  are  poles 
in  the  field.  In  every  such  case,  if  £>,  be  the  useful  flux  in 
webers  passing  from  one  pole  into  the  armature,  /,  the  total 
current  strength  delivered  to  the  armature  in  amperes,  and  w, 
the  number  of  armature  conductors  counted  once  completely 
around  its  surface,  the  torque  will  be, 

centimetre-dynes,  or 

pounds-feet. 


20   7t 

i  $  w 


20  n  x  13,550,000 
If,  however,  the  armature  be  series-connected,  so  that  there 
are  only  two  circuits  through  it,  and  there  are/,  poles  in  the 
field  frame,  the  torque  will  be 

P  i  $w  , 

• — " pounds-feet. 

2  20  n  X  13,550,000 

315.  In  a  smooth-core  armature,  the  electro-dynamic  force, 
and,  therefore,  the  torque,  is  exerted  upon  the  active  con- 
ductors, that  is  to  say,  the  force  which  rotates  the  armature 
acts  on  the  conductors  which  draw  the  armature  around  with 


MOTOR    TORQUE.  261 

them.  Consequently,  a  necessity  exists  in  this  type  of  motor 
to  attach  the  wires  securely  to  the  surface  of  the  core  in  order 
to  prevent  mechanical  displacement. 

316.  In  a  toothed-core  armature,   where    the  wires   are  so 
deeply  embedded  in  the  surface  of  the  core  as  to  be  practically 
surrounded  by  iron,  the  electro-dynamic  force  or  torque  is  ex- 
erted on  the  mass  of  the  iron  itself,  and  not  on  the  wire.    That 
is  to  say,  the  armature  current  magnetizes  the  core,  and  the  mag- 
netized core  is  then  acted  upon  by  the  field  flux.     As  soon  as 
the  iron  of  the  armature  core  becomes  nearly  saturated  by  the 
flux  passing  through  it,  the  electro-dynamic  force  will  be  exerted 
in  a  greater  degree  upon  the  embedded  conductors,  but,  under 
ordinary  conditions,  the  electro-dynamic  force  which  they  re- 
ceive is  comparatively  small.     A  toothed-core  armature,  there- 
fore, not  only  serves   to   protect  its  conductors  from  injury, 
since  they  are  embedded  in  its  mass,  but  also  prevents  their 
receiving  severe  electro-dynamic  stresses.     It  is  not  surprising, 
therefore,  that  the  tendency  of  modern  dynamo  construction 
is  almost  entirely  in  the  direction  of  toothed-core  armatures. 

317.  It  might  be  supposed  that  the  preceding  rule  for  cal- 
culating the  value  of  the  torque  in  a  motor,  whether  running 
or  at  rest,  would  only  hold  true  where  there   existed  a  fairly 
uniform  distribution  of  the  field  flux,  such  as  would  be  the  case 
where  there  was  no  marked  armature  reaction.     Observations 
appear  to   show,  however,  that  if  we  take  into  consideration 
the  actual  resultant  useful  flux  which  enters  the  armature  from 
any  pole,  the  torque  will  always  be  correctly  given  by  the  pre- 
ceding rule,  even  when  the  armature  reaction  is  very  marked. 
That  is  to  say  if  $,  be  the   total   useful  flux   passing  through 

i  $  w 
the  armature  from  one  field   pole,  the    torque  will  be  - 

20  7t 

dyne-centimetres,  no  matter  how  much  flux  may  be  produced 
independently  by  the  M.  M.  F.  of  the  armature. 

318.  We  have  hitherto  studied    the  fundamental  rules  for 
calculating  the  torque  in  the   case  of  any  continuous-current 
motor,  whether  bipolar  or  multipolar.     It  is  well  to  observe 
that  in  practice  the  torque  available  from  a  motor  at  full  load 


262  ELECTRO-DYNAMIC  MACHINERY. 

can  be  determined  without  reference  to  either  the  amount  of 
useful  flux  passing  through  the  armature,  or  to  the  amount  of 
full-load  current  strength.  'For,  if  the  full-load  output  of  a 
motor  be  P  watts,  and  the  speed  at  which  it  runs  be  ;;  revolu- 
tions per  second,  then  the  work  done  per  second  will  be 
10,000,000  P  ergs.  The  angular  velocity  of  the  shaft  will  be 
2  n  n  radians,  and  the  torque,  will,  therefore  be, 

10,000,000  P 

r  —  -  dyne-centimetres. 

2  n  n 

10,000,000    P 

t  —  pounds-feet. 

I3»55°)°00  2  TT  « 

p 

r  =  0.1174—  pounds-feet. 

For  example,  if  a  motor  gives  six  horse-power  output  at  full 
load,  and  makes  600  revolutions  per  minute,  required  its 
torque. 

Here  the  output,  />,   =  4,476  watts,  the  speed  in  revolutions 

p 
per  second  n  =  10,  —  =  447.6,  and  the  torque  exerted  by  the 

motor  at  full  load  will  be, 

t  —  0.1174  x  4,476  =  52.55  pounds-feet. 

If  the  amount  of  torque  which  the  motor  has  to  exert  in  order 
to  start  the  load  connected  with  it  never  exceeds  the  torque 
when  running  at  full  load,  then  the  current  which  will  be  re- 
quired to  pass  through  the  armature  in  order  to  start  it  will 
not  exceed  the  full  load  current. 

319.  It  is  sometimes  required  to  determine  what  amount  of 
torque  must  be  developed  by  a  motor  armature  in  order  to 
operate  a  machine  under  given  conditions.  For  example,  if  a 
machine  has  to  be  driven  with  an  activity  of  ten  horse-power,  at 
a  speed  of  300  revolutions  per  minute,  what  will  be  the  torque 
exerted  by  the  motor  running  at  900  revolutions  per  minute, 
suitable  countershafting  being  employed  between  machine  and 
motor  to  maintain  these  speeds  ?  If  we  employ  the  formula 
in  the  preceding  paragraph,  we  find  for  the  power  P  =  10  x 

746  =  7,460  watts.     The  speed  ;/  =  -= —  =  5  revolutions  per 

60 


MOTOR    TORQUE.  263 

second,  so  that  the  torque  exerted  at  the  shaft  of  the  machine 
is  r    —    0.1174  --  =0.1174  x  - —  =  175.1  pounds-feet.  The 

velocity-ratio    of  motor  to    machine    is  - —  =  3,   so  that  the 

300 

torque  exerted  by  the  motor,  neglecting  friction-torque  in  the 
countershafting  will  be  — ^-  =  58.37    pounds-feet    or    58.37 

o 

pounds  at  i  foot  radius. 

Or,  we  might  consider  that  the  motor  would,  neglecting 
frictional  waste  of  energy  in  countershafting,  be  exerting  a 

power  P  of  10  x  746  =  7,460  watts  at  a  speed  of  n  =  ~—  =  15 

revolutions  per  second.     Its  torque  would  then  be,  by  the  same 

P       0.1174  X  7,460 
formula,  r  =  0.1174  —  =  -      ' —    -  =  58.37  pounds-feet. 

320.  In  some  cases  it  is  necessary  to  determine  the  torque 
which  must  be  exerted  by  a  street-car  motor  at  maximum  load. 
It  is  not  sufficient  that  the  motor  shall  be  able  to  exert  a  maxi- 
mum activity  of  say  20  H.  P.  It  is  necessary  that  it  shall  be 
able  to  exert  the  given  maximum  torque  at  a  definite  maximum 
speed  of  rotation,  and,  therefore,  the  given  maximum  activity 
of  20  H.  P.  Otherwise,  the  motor  might  be  of  40  H.  P. 
capacity,  and,  yet  by  failing  to  exert  the  required  torque, 
might  be  unable  to  start  the  car,  or,  in  other  words,  the  motor 
would  have  too  high  a  speed. 

For  example,  required  the  torque  to  be  exerted  by  each  of  two 
single-reduction  motors  in  order  to  start  a  car  with  30"  wheels 
weighing  6  short  tons  light,  and  loaded  with  100  passengers, 
up  a  ten  per  cent,  grade,  the  gearing  ratio  of  armature 
to  car  wheel  being  3  to  i.  Here  100  passengers  may  be 
taken  as  weighing  15,000  Ibs.  or  7^  short  tons.  The  total 
weight  of  the  car  is  therefore  27,000  Ibs.  The  frictional  pull 
required  to  start  a  car  from  rest  on  level  rails,  under  average 
commercial  conditions,  is  about  1.8  per  cent,  of  the  weight,  or, 
in  this  case,  486  Ibs.  weight.  The  pull  exerted  against  gravity  is 
also  2,700  Ibs.,  making  the  total  pull  3,186  Ibs.  weight.  The 

radius  of  the  car  wheel  being—  =  1.25  feet,  the  torque  at  the  car 

24 


264  ELECTRO-DYNAMIC  MACHINERY. 

wheel  axle  is  3,186  x  1.25  =  3,983  pounds-feet.     The  torque 

at  the  motor  shafts  is  therefore  3>9  3  =  1,328  pounds-feet,  and 

each  motor  must  therefore  exert  I^-  =  664  pounds-feet. 

If  the  motors  make  600  revolutions  per  minute  or  10  revolu- 
tions per  second,  exerting  this  torque,  their  activity  will  be 
664  x  10  x  2  TT  X  1.355  =  56>53°  watts,  =  56.53  KW,  and 
their  combined  activity  113.1  KW,  neglecting  gear  frictions. 


321.  Considering  the  case  of  a  motor  armature  in  rotation, 
the  speed  of  its  rotation  for  a  given  E.  M.  F.  applied  to  its 
armature  terminals  will  depend  upon  three  things  :  viz., 

(i.)  The  load  imposed  upon  the  armature,  or  the  torque  it 
has  to  exert. 

(2.)  The  electric  resistance  of  the  armature  in  ohms. 

(3.)  Its  dynamo-power ;  i.  e.,  its  power  of  producing  C.  E. 
M.  F.,  or  the  number  of  volts  it  will  produce  per  revolution 
per  second. 

If  £,  be  the  E.  M.  F.  in  volts  applied  to  the  armature  termi- 
nals, T,  the  torque,  which  the  motor  has  to  exert,  including 
the  torque  of  frictions,  in  megadyne-decimetres  (dyne-cms.  X 
io~7)  r,  the  resistance  of  the  motor  armature  in  ohms,  and  e,  the 
C.  E.  M.  F.  produced  in  volts  per  revolution  per  second  of  the 

armature.     Then  n  e,  will  be  the  total  C.  E.  M.  F.  . —  ~-^-  will 

be  the  current  strength   received  by  the  armature  according 
to  Ohm's  law.      The  activity  of  this  current  expended  upon 

'      9  //*    ^2   P 

the    C.    E.   M.    F.    will    be    their    product,   or    n  e  x  - 

watts,  and  this  must  be  equal  to  the  total  rate  of  working,  or 

/£  —  n  e\ 
2   7t  n  T,    =     consequently,    n  e  f J  =    2   n   n  t    and 

E  r-c 

n  — 2  it  — r  revolutions  per  second. 

For  example,  if  a  motor  armature,  whose  resistance  is  2 
ohms,  has  a  uniformly  excited  field,  which  may  be  either  of  the 
bipolar  or  multipolar  type,  and  is  supplied  with  500  volts  at 
its  terminals  ;  and  if  the  C.  E.  M.  F.  it  produces  by  revolution 
in  the  field  is  40  volts  per-revolution-per-second,  then  the  speed 


MOTOR    TORQUE.  265 

at  which  the  motor  will  rotate,  when  exerting  a  torque,  including 
all  frictions,  of  100  pounds-feet  (100  x  13,550,000  dyne-centi- 
metres, =  135.5  megadyne-decimetres)  will  be 

500  27T    X    2X    135-5 

n  =  -  =  12.5  —  i. 06  =  11.44  revolutions- 

40  1,600 

per-second. 

322.  It   will   be   observed  from  the   above   formula   that  if 
either  the  torque  be  zero,  or  the  resistance  of  the  armature  is 

Tf 

zero,  the  speed  of  the  motor  will  simply  be  —  revolutions-per- 

second.  Or,  in  other  words,  that  the  armature  will  run  at 
such  a  speed  that  its  C.  E.  M.  F.  shall  just  equal  the  E.  M.  F. 
applied  to  the  armature  ;  **.  e.  without  drop  of  pressure  in  the 
armature.  If  the  torque  could  be  made  zero,  the  motor 
would  do  no  work  and  would  require  no  current  to  be  supplied 
to  it,  so  that  no  matter  what  the  resistance  of  the  armature 
might  be,  the  drop  in  the  armature  would  be  zero.  All 
motors  necessarily  have  to  exert  some  torque  in  order  to  over- 
come various  frictions,  but  on  light  load  their  speed  approxi- 

£ 

mates  to  the  value  —  revolutions-per-second.  If  the  resistance 
of  the  motor  is  very  small,  which  is  approximately  true  in 
the  case  of  a  large  motor,  the  second  term ^ — ,  in  the 

formula,  becomes  small,  and  the  diminution  in  speed  due  to 
load  is,  therefore,  also  small.  In  other  words,  the  drop  which 
takes  place  in  the  armature  due  to  its  resistance  is  correspond- 
ingly reduced,  permitting  the  motor  to  maintain  its  speed  and 
C.  E.  M.  F.  of  rotation.  Fig.  209  represents  diagrammati- 
cally  a  motor  armature  revolving  in  a  suitably  excited 
magnetic  field,  and  supplied  from  a  pair  of  mains,  J/,  M,  with 
a  steady  pressure  of  500  volts.  The  resistance  of  the  arma- 
ture is  represented  as  being  collected  in  the  coil  r,  while  the 
C.  E.  M.  F.  of  the  motor  is  indicated  as  opposing  the  passage 
of  the  current  from  the  mains. 

The  drop  in  the  resistance  is  represented  as  being  40  volts, 
while  the  C.  E.  M.  F.  is  500  —  40,  or  460  volts. 

323.  The   E.    M.    F.   applied  to    the   terminals  of   a   motor 
armature,  therefore,  has  to  be  met  by  an  equal  and  opposite  or 


266 


ELECTRO-D  YNAMIC  MA  CHINEX  Y. 


C.  E.  M.  F.  in  the  armature,  which  is  composed  of  two 
parts,  that  due  to  rotation  in  the  magnetic  flux,  or  to  dynamo- 
electric  action,  and  that  apparent  C.  E.  M.  F.  which  is 
entirely  due  to  drop  of  pressure  in  the  resistance  of  the  arma- 
ture, considered  as  an  equivalent  length  of  wire.  The  activity 
expended  against  the  C.  E.  M.  F.  of  rotation  is  activity 
expended  in  producing  torque,  and,  therefore,  almost  all 
available  for  producing  useful  work,  while  the  activity  expended 
against  the  C.  E.  M.  F.  of  drop  is  entirely  expended  in  heating 
the  wire.  As  the  load  on  the  motor  is  increased,  the  current 


FIG.    209. — DIAGRAM    REPRESENTING   RESISTANCE   AND    C.    E.    M.    F.    IN   A 
REVOLVING   MOTOR-ARMATURE. 


which  must  be  supplied  to  the  motor  to  overcome  the  addi- 
tional load  or  torque  increases  the  drop  in  the  armature,  and, 
therefore,  diminishes  the  C.  E.  M.  F.  which  has  to  be  made  up 
by  rotation,  and  the  speed  falls,  or  tends  to  fall,  in  proportion. 

324.  When  a  motor  armature  is  at  rest,  its  C.  E.  M.  F.  of 
rotation  is  zero,  and  the  C.  E.  M.  F.  which  it  can  produce 
under  these  conditions  must  be  entirely  composed  of  drop  of 
pressure.  In  other  words,  the  current  which  will  pass  through 
it  is  limited  entirely  by  the  ohmic  resistance  of  the  circuit. 

If  /,  be  the  current  strength  in  amperes  supplied  to  a  motor 
armature  at  a  pressure  of  E  volts,  the  activity  expended  in  the 
armature  will  be  E  i  watts.  The  activity  expended  in  produc- 


MOTOR    TORQUE.  267 

ing  torque  will  be  //  e  i  watts,  so  that  disregarding  mechanical 
and  electro-magnetic  frictions,  the  efficiency  of  the  motor  will 

be  -y^-r  =  -=-,  or  simply  the  ratio  of  the   C.  E.  M.  F.  of  rota- 
&  l  Jc, 

tion  to  the  impressed  E.  M.  F.  This  is  a  maximum  at  no 
load  ;  /.  e.,  when  the  motor  does  no  work,  and  is  zero  when 
the  motor  is  at  rest. 

The  value  of  e,  the  volts-per-revolution-per-second,  is  in  all 
cases  of  multiple-connected  armatures  equal  to  0  w  x  I0~8, 
where  $,  is  the  number  of  webers  of  flux  passing  usefully  into 
the  armature  from  any  one  pole,  and  «/,  is  the  number  of  turns 
of  conductor  counted  once  around  its  periphery. 

325.  The  speed  of  a  motor,  therefore,  varies,  to  the  first  ap- 
proximation,   inversely   as    the   useful   magnetic  flux,  and  in- 
versely as  the  number  of  armature  conductors.     A  slow-speed 
motor,  other  things  being  equal,  is  a  motor  of  large  flux,  or  large 
number  of  turns,  or  both,  and,  as  will  afterward  be  shown,  in 
order  to  decrease  the  speed  at  which  the  motor  is  running,  it 
is  only  necessary  to  increase,  by  any  suitable  means,  the  use- 
ful flux  passing  through  its  armature. 

326.  Just  as  in  the  case  of  a  generator  armature,  whose 
maximum  output  is  obtained  when  the  drop  in  its  armature  is 
equal  to  half  its  terminal  E.  M.  F.  (Par.  9),  so  in   the  case  of 
the  motor,  the"  output  is  a  maximum  (neglecting   frictions), 
when  the  drop  in  the  armature  is  half  the  E.  M.  F.  applied  at 

TT> 

the    armature  terminals,  or,  in  symbols,  when  n  e  =  — ;   the 

2 

speed  of  the  motor  being  then  half  its  theoretical  maximum 
speed,  assuming  no  friction. 

Similarly,  just  as  it  is  impracticable  to  operate  a  generator 
of  any  size  at  its  maximum  theoretical  output,  since  the  activity 
expended  within  it  would  be  so  great  as  probably  to  destroy  it, 
being  equal  to  its  external  activity,  so  no  motor  of  any  size 
can  be  operated  so  as  to  give  the  maximum  theoretical  output 
of  work,  since  the  activity  expended  in  heating  the  machine, 
being  equal  to  its  output,  would,  probably,  cause  its  destruc- 
tion. 


CHAPTER  XXVI. 

EFFICIENCY    OF    MOTORS. 

327.  As  in  the  case  of  generators,  the  commercial  efficiency  of 
the  electric  motor  is  the  ratio   of  the  output  to  the  intake: 
that  is, 

Output 
EfficienC^:  Intake- ' 

Since  the  output  must  be  equal  to  the  intake  after  subtracting 
the  loss  taking  place  in  the  machine,  the  above  may  be 
expressed  as  follows: 

Intake  —  Losses 
Efficiency  =  - 

Intake 

328.  The  losses  which  occur  in  a  motor  are  of  the  same 
nature  as  those  already  pointed  out  in  Par.  224,  in  connection 
with  a  generator.     This  is  evident  from  the  fact  that  a  motor 
is  but  a  generator  in  reversed  action;  so  that  any  dynamo  is 
capable  of  being  operated,  either  as  a  generator  or  as  a  motor, 
according  as  the  driving  power  is  applied  to  it  mechanically  or 
electrically.     There  is  this  difference,   however,  between  the 
two  cases,  that  a  very  small  dynamo-electric  machine  may  be 
capable  of  acting  as  a  motor,  while  it  is  not  capable  of  acting 
as  a  dynamo,  owing  to  the  fact  that  it  is  not  able,  unaided,  to 
excite  its  own  field   magnets,    its  residual    magnetism  being 
insufficient  for  this  purpose.     On  this  account,  motors  can  be 
constructed  of  much  smaller  sizes  than  self-exciting  generators. 

329.  If  the  losses  which  occur  in  a  dynamo-electric  machine, 
acting  as  a  generator,    have  been  determined,   we  can  then 
closely  estimate  what  these  losses  will  be  when  the  machine  is 
operated  as  a  motor,  and,  consequently,  the  efficiency  of  the 
machine  as  a  motor  can  be  arrived  at. 

330.  There  is  this  difference  between  a  dynamo  and  a  motor 
as  regards  the  output;  viz.,  in  the  dynamo,  the  energy  lost  is 


EFFICIENCY  OF  MOTORS.  269 

•derived  from  the  driving  source,  while  in  the  motor  the  energy 
lost  is'derived  electrically  from  the  circuit;  but  the  output  of 
.a  dynamo-electric  machine  is  almost  invariably  determined  by 
the  electric  activity  in  its  armature  circuit;  that  is  to  say,  the 
.armature  is  limited  to  a  certain  number  of  amperes  received 
or  delivered  at  a  certain  number  of  volts  pressure,  so  that 
since  this  load  is  the  output,  when  the  machine  is  a  generator, 
and  the  intake,  when  the  machine  is  a  motor,  it  is  evident  that 
.after  the  losses  as  a  motor  have  been  subtracted,  the  mechani- 
cal output  will  be  less  than  the  electrical  output  which  the 
machine  produces  as  a  generator. 

331.  For   example,  let  us  suppose  that  a  certain  machine, 
-acting  as  a  series-wound  generator,  is  capable  of  delivering  10 
.amperes  at  a  pressure  of  100  volts,  so  that  its  output  is  i  KW. 
Let  us  also  suppose  that  when  acting  as  a  generator,  a  loss  of 
250  watts  occurs,   in  friction,  hysteresis,    eddy  currents  and 
PR  losses,   both   in  the  armature  and  in  the  field;  then  the 
mechanical  intake  of  the  machine  will  be  1,250  watts,  and  its 

commercial    efficiency,  — =  0.8,  or  80   per  cent.      When, 

however,  the  machine  is  operated  as  a  motor,  the  armature  is 
limited  to  the  same  current  strength  of  10  amperes,  and  the 
pressure  at  the  machine  terminals  can  only  be  slightly  in 
excess  of  the  100  volts  previously  delivered.  Let  us  suppose 
that  this  is  no  volts.  Then  the  intake  of  the  machine  will  be 
1,100  watts.  Assuming  the  same  losses  as  before;  namely, 
250  watts,  the  output  would  be  only  850  watts,  and  the 

•efficiency,  therefore,  -      -  =  0.772,  or  about  2^  per  cent,  less 

than  in  the  preceding  case.  It  is  clear,  therefore,  that  while 
the  output  of  the  machine  was  1,000  watts  when  acting  as  a 
generator,  it  was  limited  to  850  watts  'when  acting  as  a  motor, 
assuming  that  the  same  limiting  armature  temperature  and 
same  liability  to  sparking  were  accepted  in  each  case. 

332.  The  difference  above  pointed  out  between  the  output  of 
a  machine  acting  as  a   generator  and  as  a  motor,  diminishes 
with  an  increase  in  the  size  of  the  machine.     Thus,  while  a 
j-KW  generator  is  usually  only  a  i-H.  P.  motor  (or  has  an  out- 


270 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


put  of  say  750  watts),  a  generator  of  200  KW  would,  probably,. 
be  a  motor  of  185  H.  P. ;  so  that  in  the  case  of  very  large 
machines,  the  difference  between  the  outputs  in  the  two  cases 
would  be  practically  negligible. 

333.  The  curve  in  the  accompanying  Fig.  210,  approximately 
represents  the  efficiency  which  may  be  expected  at  full  load 

4 
100 


95 


5 

Li. 
U. 

? 
§ 

£65 


/ 

^  — 

—as 

MMER 

DIALJ 

FFICjj 

NOY_ 

-       — 

/ 

25        50        75       100      125      1 

—  '-—-                       IOI  ftWATTR  OUTPUT 

jO      175     20( 

KILOWATTS  OUTPUT 
FIG.    210. — COMMERCIAL   EFFICIENCY    CURVE   OF   MOTORS   AT   FULL   LOAD. 


from  motors  of  varying  capacity  up  to  200  KW.  This  curve 
has  been  plotted  from  a  number  of  actual  observations  with 
machines  constructed  in  the  United  States. 

334.  It  is  to  be  remembered,  however,  that  the  full  load 
efficiency  of  a  motor  is  not  always  the  criterion  upon  which  its 
suitability  for  economically  performing  a  given  service  is  to  be 
determined.  It  not  infrequently  happens  that  the  character  of 
the  work  which  a  motor  has  to  perform  is  necessarily  exceed- 
ingly variable,  so  that  the  average  load  might  not  be  half 
the  full  load  of  the  machine.  Under  such  conditions,  the 
average  efficiency  is  of  more  importance  than  the  full-load* 
efficiency.  Were  the  efficiency  curve  of  all  motors  in  relation. 


EFFICIENCY  OF  MOTORS.  271 

to  their  load  of  the  same  general  outline,  the  average  efficiency 
would  be,  approximately,  the  same  in  all  motors  having  the 
same  full-load  efficiency.  As  a  matter  of  fact,  however,  the 
efficiency  curves  of  different  machines  may  be  very  different. 
Thus  one  machine  may  have  its  maximum  efficiency  at  half 
load,  and  behave  at  full  load,  in  regard  to  its  efficiency,  as 
though  it  were  actually  overloaded,  while  another  machine, 
with  the  same  full-load  efficiency,  may  show  a  lower  efficiency 
at  half  load.  Obviously  the  first  machine  would  be  preferred 
for  variable  work,  other  things  being  equal 

335.  Similar  considerations    apply  to    electric   generators. 
The  full-load    efficiency    is  not    in    every   case   the   ultimate 
criterion   of  economical  delivery   of    work,   but  it  generally 
happens  that  generators  are  installed  in  such  a  manner,  and 
under  such  conditions,  that  a  nearer  approach  to  their  full  load 
is  attained,  so  that  ordinarily  the  shape  of  the  efficiency  curve 
of  a  generator  is  not  of  such  great   importance  as  that  of  a 
motor. 

Fig.  211  represents  the  efficiency  curves  of  two  motors,  each 
having  a  full-load  efficiency  of  78  per  cent.  One  of  these 
machines  has  an  efficiency,  at  about  two-thirds  load,  of  84  per 
cent.,  but  at  overloads  is  inefficient,  while  the  other  becomes 
more  efficient  at  slight  overloads. 

336.  In  order  to  produce  a  motor  of  given  full-load  efficiency 
with  comparatively  small  loss  at  moderate  loads,  and,  there- 
fore, a  comparatively  heavy  loss  at  heavy  loads,  we  may  em- 
ploy a  slow-speed  motor,  or  a  motor  which  shall  generate  the 
necessary  C.  E.  M.  F.  at  a  comparatively  low  speed.     Such  a 
machine  will  probably  have  a  small  loss  in  mechanical  friction, 
because  of  its  lower  speed  of  revolution.     It  will,   similarly, 
have,  probably,  a  small  loss  in  hysteresis  and  eddy  currents 
for  the  same  reason,   but  a  slow  speed  motor  will   probably 
have  a  greater  number  of  armature  turns  in  order  to  com- 
pensate for  the  smaller  rate  of  revolution,  and  the  I*R  loss  in 
the  armature  is,  therefore,  likely  to  be  greater  at  full  load.     In 
such  a  machine,  the  loss  at  full  load  is  principally  due  to  PR; 
and,  since  this  loss  decreases  rapidly  with  7,  it  will  evidently 
have  a  small  loss  at  moderate  loads. 


272 


ELECTRO-DYNAMIC  MACHINERY. 


337;  The  speed  at  which  a  motor  will  run  in  performing  a 
given  amount  of  work  varies  considerably  with  different  types 
of  motors.  For  example,  of  two  motors  of  20  KW  capacity, 
one  may  run  at  400  revolutions-per-minute,  and  the  other  at 
1,000  revolutions-per-minute.  It  is  evident  that  the  first 
machine  will  have  two  and  a  half  times  the  full-load  torque  of 
the  second.  The  lower  speed  is,  however,  generally  speaking, 
only  to  be  obtained  at  the  expense  of  additional  copper  and 
iron  ;  that  is  to  say,  the  cost  of  material  in  a  slow-speed 
machine  will,  probably,  be  greater  than  the  cost  of  material 


100 


It 


PROPORTION  OF  LOAD  g 

FIG.  211. — EFFICIENCY   CURVES   OF   TWO    DIFFERENT   MOTORS   HAVING   SAME 
FULL-LOAD   EFFICIENCY. 


in  a  high-speed  machine  of  the  same  output  and  relative  excel- 
lence of  design.  It  becomes,  therefore,  a  question  as  to  the 
relative  commercial  advantage  of  slow  speed  versus  high  speed 
in  a  motor. 

338.  Motors  are  generally  installed  to  drive  machinery  either 
by  belts  or'  gears,  and  the  belt  speed  or  the  gear  speed  of 
machinery  is,  in  practice,  a  comparatively  fixed  quantity.  If, 


EFFICIENCY  OF  MOTORS.  273 

therefore,  the  speed  of  the  motor  be  greater  than  the  speed  of 
the  main  driving  wheel  of  the  machines  with  which  the  motor 
is  connected,  intermediate  reducing  gear  or  countershafting  has 
to  be  installed.  This  adds  to  the  expense  of  installation,  not 
only  in  first  cost,  but  also  in  maintenance,  lubrication,  and  the 
•continuous  loss  of  power  it  introduces  through  friction.  The 
result  is,  that  up  to  a  certain  point,  slow-speed  motors  are 
•economically  preferable,  and  the  tendency  of  recent  years  has 
been  toward  the  production  of  slower  speed  dynamo  machinery. 
In  comparing,  therefore,  the  prices  of  two  motors  of  equal 
output,  the  speed  at  which  they  run  has  to  be  taken  into 
account,  as  well  as  the  efficiency  at  which  they  will  operate. 
It  is  to  be  remembered  that  any  means  in  the  design  which 
will  enable  a  motor  to  supply  its  output  at  a  slower  speed,  are 
-equivalent  to  means  which  will  enable  a  motor  of  the  higher 
speed  to  supply  a  greater  output. 

339.  The  weight  of.a  motor  is  a  matter  of  considerable  im- 
portance in  cases  of  loco  motors  /  /'.  e.,  of  travelling  motors,  as  in 
the  case  of  electric  locomotives,  street-car  motors  or  launch 
motors,  but  in  the  case  of  stationary  motors,  their  weight  is  of 
less  consequence,   since,   after  freight  has  been  once  paid  for 
their  shipment,  no  extra  expense  is  entailed  by  reason  of  their 
increased  mass  when  in  operation.     Indeed,  weight  is  often  a 
-desirable  quality  for  a  motor  to   possess  in  order  to  ensure 
steadiness  of  driving,  although  undue  weight  in  the  armature 
is  apt  to  produce  frictional  loss,  and  diminished  efficiency. 

340.  In  comparing  the  relative  weights  of  motors,  two  cri- 
teria may  be  established;   namely, 

(i)  In  regard  to  torque,  and  (2)  in  regard  to  activity.  In 
some  cases,  the  work  required  from  the  motor  is  such  that 
the  pull  or  torque  which  must  be  given  in  reference  to  its 
weight  is  the  main  consideration,  while  in  other  cases  it  is  not 
the  torque,  but  the  output  per-pound  of  weight,  which  must  be 
considered. 

341.  The  torque-per-pound,  in  the  case  of  street-car  motors, 
where  lightness  is  an  important  factor,  has  been  increased  to 


274  ELECTRO-DYNAMIC  MACHINERY. 

133,000  centimetre-dynes  per-ampere,  per-kilogramme  of 
weight;  or,  0.0045  pound-foot  per-ampere  per-pound  of  total 
motor  weight,  exclusive  of  gears,  so  that  a  5oo-volt  street-car 
motor,  weighing  223  pounds,  and  supplied  with  one  ampere  of 
current,  would  exert  a  torque  of  one  pound-foot.  In  stationary 
motors,  the  torque  is  usually  only  o.ooi  to  0.0015  pound-foot 
per-ampere  per-pound  of  .weight,  or  about  four  times  less  than 
with  street-car  motors.  This  is  owing  to  the  fact  that  cast 
iron  is  more  largely  employed  in  stationary  motors,  owing  to 
its  lesser  cost. 

The  output  per-pound  of  weight  in  motors  varies  from  5 
watts  per  pound  to  15  watts  per  pound,  according  to  the  size 
and  speed  of  the  motor. 

342.  We   may     now   allude    to   the   theoretical   conditions 
which  must  be  complied  with  in  order  to  obtain  the  maximum 
amount  of  torque  in  a  motor  for  a  given  mass  of  material.      It 
must  be  carefully  remembered,  however,  that  these  theoretical 
conditions  require  both   modification  and  amplification,  when 
applied  to  practice,  so  that  the  practical  problem  is  the  theo- 
retical  problem   combined   with   the   problem    of   mechanical 
construction. 

/  ^  iu 

343.  The  torque  of  a  motor  armature  being   — -  cm.- 

dynes,  we  require  to  make  this  expression  a  maximum  for  a 
given  mass  of  copper  wire  in  the  armature  and  in  the  field 
magnets,  neglecting  at  present  all  considerations  of  structural 
strength. 

^  w 
The  torque-per-ampere  will  be cm. -dynes. 

2O  7t 

In  order  to  make  this  a  maximum,  both  #  and  w,  should  be 
as  great  as  possible. 

344.  It  is  evident  that  if  we  simply  desired  a  motor  of  power- 
ful   torque-per-ampere,    regardless    of    its   weight,    we    should 
employ  as  much  useful  iron  as   possible,   so  as  to   obtain  as 
great   a   useful    magnetic     flux    #,  through    the   armature,   as 
possible,  and  we   should  employ  as  many  turns  of  wire  upon 
the  surface  of  the  armature  as  could  be  obtained  without  mak- 


EFFICIENCY  OF  MOTORS.  275 

ing  the  armature  reaction  excessive,  or  without  introducing 
too  high  a  resistance,  and  too  much  expenditure  of  energy  in 
the  armature  winding.  Such  a  motor  would  essentially  be  a 
heavy  motor,  so  that  the  requirements  of  a  motor  with  power- 
ful torque-per-ampere  would  simply  be  met  by  a  motor  of  great 
useful  weight,  and  this,  indeed,  would  be  obvious  without  any 
arithmetical  reasoning. 

345.  When,   however,  the  torque-per-ampere   per-pound-of- 
weight  has  to  be  a  maximum,  the  best  means  of  attacking  the 
problem  is  to  consider  a  given  total  weight  of  copper  and  iron 
in  the  armature,  and  examine  by  what  means  this  total  weight 
can  be  most  effectually  employed  for  producing  dynamo-power; 
i,  <?.,  volts-per-revolution-per-second,  and  torque-per-ampere. 

346.  It  will,  in  the  first  place,  be  obvious  that  a  long  mag- 
netic circuit  will  not  be  consistent  with   these  requirements, 
since,  as  we   shorten  the   magnetic  circuit,  retaining  the  same 
mass  of  material,  we  make  it  wider,  or  of  greater  section,  and 
so  increase  the  total  flux  ^.     In  the  second  place,  the  material 
of  which  the  magnetic  circuit  is  formed  should  have  as  small  a 
reluctivity,   and  as  powerful   a  flux  density  as  possible,  since 
this  will  increase   the  total  flux  without  adding  to  the  weight. 
For  this  reason  soft  cast  steel  is  much  to  be  preferred  to  cast 
iron. 

347.  Again,  it  will  be  evident  that  as  we  increase  the  number 
of  turns   on  the  armature,  having  determined  upon  a  certain 
total  mass  of  armature  copper,  or  armature  winding  space,  we 
increase,  according    to  the    formula,  the    torque-per-ampere. 
But,  in  occupying  the  given  winding  space  with   many  turns 
instead  of  with  few  turns,  we  increase,  for  a  given  speed,  the 
voltage  of  the  armature.     Thus,  if  a  motor  armature  be  intended 
to  rotate  at  a  speed  of  10  revolutions  per  second,  its  E.  M.  F., 
other  things  being  equal,  will  be  10  times  as  great,  when  we 
use  10  times  as  many  wires  upon  its  surface,  and  its  torque- 
per-ampere  will  be  also  increased  10  times.     A  high  E.  M.  F. 
motor  is,  therefore,  necessarily  a   motor  of  high  torque-per- 
ampere.     A  5oo-volt  armature  would,  therefore,  in  accordance 
with  preceding  principles,    necessarily  be  a  motor  of  greater 


276  ELECTRO-DYNAMIC  MACHINERY. 

torque-per-ampere  than  the  same  armature  wound  for  100  volts, 
although  the  torque  at  full  load  might  be  the  same  in  each 
case,  since  the  low-pressure  armature  might  make  up  by  in- 
crease of  current  what  it  lacked  in  torque-per-ampere. 


348.  Having  selected  a  field  frame  with  as  short  a  magnetic 
circuit  as  is  consistent  with  not  excessive  magnetic  leakage, 
and  with  room  for  magnetizing  coils,  and  having  placed  a  large 
number  of  turns    upon    the  armature  surface,    there   remain 
several  important  detail  considerations  which  should  be  taken 
into  account  to  enable  a  high  torque-per-ampere  to  be  obtained. 

349.  In  the  first  place,  the  reluctance  in  the  magnetic  circuit 
should  be  as  small  as  possible  in  order  to  diminish  the  M.  M.  F. 
and   the  mass    of    magnetizing    copper.      With    smooth-core 
armatures  this  would  represent  a  small  entrefer  and  a  small 
winding  space,  whereas,  to  obtain   many    turns,  we  require  a 
large  entrefer  and  large  winding  space,  so  that  with  a  smooth- 
core  armature,   a  compromise    is  necessary  at   some  point  of 
maximum  effect,   depending  upon  a  great  variety  of   details. 
With    toothed-core   armatures,    however,    a    large    number  of 
turns  may  be  disposed    upon  the   armature   surface,    yet  the 
reluctance  in  the  entrefer  may  be  comparatively  small.     This 
consideration   affords    an    additional     argument   in    favor   of 
toothed-core  armatures  for  high  torque. 

350.  In  the  second  place,  the  number  of  poles  in  the  field 
frame  should  be  as  great  as  possible.     If  we  double  the  number 
of  poles  in  the  field  frame,  retaining  the  same  armature,  and 
make  suitable  changes  in  the  connection  of  the  armature  turns, 
we  double  the  E.  M.  F.  of  the  armature  (Par.  148).     Thus,  if  we 
have  an  armature  with  a  given  number  of  turns  on  its  surface 
and  a  given  speed  of  rotation,  in  a  bipolar  field,  and  the  E.  M.  F. 
obtained  from  the  armature   is   100  volts,  then,  if  we  change 
the  field  to  a  quadripolar  frame,  and  suitably  change  the  con- 
nection of  the  armature  turns,  the  E.  M.  F.  of  the  armature 
will  be  200  volts.     If,  instead  of  changing  the  armature  con- 
nections, we  simply  change  the  number  of  brushes  from  two  to 
four,  and   suitably  connect  these  brushes,  we  obtain  only  100 


EFFICIENCY  OF  MOTORS.  277 

volts  as  before,  but  as  there  are  now  four  complete  electric 
circuits  through  the  armature,  we  have  doubled  the  load  which 
the  armature  can  sustain  without  overheating,  and,  therefore, 
practically  doubled  the  output  of  the  armature,  so  that  when  we 
double  the  number  of  poles  covering  the  armature,  assuming 
the  useful  flux  through  each  pole  to  be  the  same  as  before,  we 
either  double  the  torque-per-ampere  directly,  if  the  armature 
be  series-connected,  or  we  retain  the  torque-per-ampere  with 


FIG.    212. — QUADRIPOLAR    CAR    MOTOR    WITH    TWO    FIELD    COILS. 

a  multiple-connected  armature  and,  by  changing  the  winding, 
obtain  a  greater  output  from  the  motor. 

351.  There  will,  of  course,  be  a  limit  to  the  number  of  poles 
which  can  be  employed  writh  any  armature  without  increasing 
its  diameter,  since  there  will  only  be  sufficient  room  for  a  cer- 
tain number  of  poles  carrying  a  given  maximum  flux,  and  also, 
since  the  difficulty  of  magnetizing  a  greater  number  of  poles 
will   be   insuperable,   either  for  want  of  space,    or   owing   to 
increased    magnetic    leakage.      The    principle,    however,     is 
important. 

352.  .The  number  of  turns  which  can  be  utilized  upon  the 
surface  of  an  armature  is  itself  limited;  first,  by  the  resistance 


278 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


of  the  armature  and  consequent  excessive  heating  under  load; 
second,  by  excessive  armature  reaction  and  consequent  spark- 
ing ;  and,  third,  in  rarer  cases,  by  the  E.  M.  F.  of  the  circuit, 


FIG.    213. — QUADRIPOLAR    CAR   MOTOR   WITH   FOUR    FIELD   COILS. 

and,  consequently,  the  unduly  slow  speed  at  which  a  powerful 
armature  will  run  on  such  circuit. 

353.  The  best  embodiment  of  the  foregoing  principles  in  ex- 
isting practice  is  found  in  a  modern  street-car  motor.  Here  a 
powerful  torque-per-ampere,  with  minimum  weight,  is  desired 
in  order  to  start  a  loaded  car  from  rest  up  a  steep  gradient. 

Two  forms  of  such  motors  are  shown  in  Figs.  212  and  213. 

354-  Fig-  2I2  shows  a  cast-steel  quadripolar  field  frame  with 
two  magnetizing  coils  M,  M.  These  produce  not  only  poles 
at  the  opposite  sides  of  the  armature,  in  the  cores  over  which 


EFFICIENCY  OF  MOTORS.  279 

they  are  wound,  but  also  poles  at  the  cylindrical  projections 
P,  P,  which  lie  above  and  below  the  armature  so  that  there 
are  four  complete  magnetic  circuits  through  the  field  frame 
and  armature,  two  circuits  through  each  magnetizing  coil. 
The  brushes  B,  B,  are  set  90  degrees  apart  on  the  commutator 
C.  The  armature  A,  is  of  the  toothed-core  type. 

355.  In  Fig.  213  the  same  results  are  obtained  with  various 
detailed  differences  in  mechanical  construction.  There  are 
four  poles  around  the  armature,  two  of  which,  P,  P,  are  seen 
in  the  raised  cover,  and  two  others  are  similarly  contained  in 
the  lower  half  of  the  frame.  Each  of  these  poles  is,  in  this 
case,  surrounded  by  a  magnetizing  coil,  M.  B,  B,  are  the 
brushes,  set  90°  apart  from  the  commutator.  The  armature, 
A,  is  of  the  toothed-core  type. 

In  both  of  these  cases  the  magnetic  circuits  are  as  short  as 
is  practically  possible,  and  the  useful  magnetic  flux  is  as  great 
as  possible. 


CHAPTER  XXVII. 

REGULATION    OF    MOTORS. 

356.  The  requirements  of  a  motor  depend  upon  the  nature 
and  use  of  the  apparatus  which  the  motor  is  designed  to  drive. 
All  these  requirements,  in  relation  to  driving  machinery,  may 
be  embraced  under  three  heads;  viz., 

(i.)  Control  of  starting  and  stopping. 

(2.)  Control  of  speed,  both  as  to  constancy  and  as  to  vari- 
ability. 

(3.)  Control  of  torque,  both  as  to  constancy  and  as  to 
variability. 

The  above  requirements  are  by  no  means  met  to  an  equal 
degree  by  the  electric  motor. 

For  example,  the  requirement  of  constant  speed  is  much 
more  readily  dealt  with  than  the  requirement  of  variable  speed. 

357.  The  conditions  under    which  motors  have  to  operate 
may  be  divided  into  four  classes;  namely, 

(i.)  Constant  torque  and  constant  speed. 
(2.)  Variable  torque  and  constant  speed. 
(3.)  Constant  torque  and  variable  speed. 
(4.)  Variable  torque  and  variable  speed. 

358.  The  first  two  conditions  are  readily  secured,  the  third 
and  fourth   are   only  secured  with  difficulty.     For  example,  a 
rotary  pump  belongs  to  the  first  class.     Here  the  load  is  con- 
stant and  the   speed  is  presumably  constant. 

The  second  class  comprises  the  greater  number  of  machine 
tools,  where  the  speed  is  constant  but  the  activity  is  variable. 

The  third  class  embraces  most  elevators  and  hoisting  ma- 
chines. 

The  fourth  class  is  well  represented  by  street-car  motors. 

359.  Any  continuous-current   electric  motor  will    supply  a 
constant  torque  at  a  constant  speed  when  operated  at  a  constant 

280 


REGULATION   OF  MOTORS. 


281 


pressure.  Thus,  whether  the  motor  be  self-excited  or  sep- 
arately-excited, and  whether  it  be  shunt-wound,  series-wound 
or  compound-wound,  it  will,  if  supplied  with  a  constant  pres- 
sure at  its  terminals,  and  assuming  constant  frictions  in  the 
machine,  deliver  a  constant  torque  at  a  constant  speed,  and 
taking  from  the  mains  supplying  it,  a  constant  current  strength, 
and,  therefore,  constant  activity.  The  condition  of  constant 
torque  and  constant  speed  is  one  which  is,  therefore,  readily 
dealt  with  by  electric  motors. 

The  above  statement,  however,  is  true  only  of  single  motors; 
for,  if  two   motors,  of  any  continuous-current  type,    be  con- 


FIG.    214. — TWO    SERIES-WOUND    MOTORS    COUPLED    IN    SERIES    BETWEEN 
CONSTANT-POTENTIAL   MAINS. 

nected  in  series  across  a  pair  of  constant-potential  mains,  they 
will  be  in  unstable  equilibrium  as  to  speed  under  a  given  load. 
If  the  torque  on  each  of  the  two  machines  in  Fig.  214  were 
maintained  absolutely  equal;  then,  by  symmetry,  the  two  series 
motors  represented  would  run  at  equal  speeds,  and  absorb 
equal  activities.  But  should  the  load  on  one  accidentally 
increase,  even  to  a  small  extent,  above  that  of  the  other,  the 
tendency  would  be  to  slow  down  the  over-loaded  motor  and 
accelerate  the  other,  so  that  it  would  be  possible  to  have  one 
motor  at  rest  exerting  a  constant  torque,  and  the  other  motor 
exerting  the  same  torque  at  double  its  former  speed.  If,  how- 
ever, the  two  motors  are  rigidly  coupled  together  to  a  coun- 
tershaft, so  that  their  speeds  must  be  alike,  then  they  will 
behave  as  a  single  motor.  Consequently,  a  continuous-current 
motor  employed  for  pumping  or  driving  a  fan,  and  which,  there- 


282  ELECTRO-DYNAMIC  MACHINERY. 

fore,  has  a  constant  torque  to  supply,  will  run  at  constant  speed 
when  supplied  with  constant  pressure,  whatever  the  type  of 
motor  may  be. 

360.  The    important   requirement  of  constant  speed  under 
variable   load  is  nearly  met  by  a  shunt-wound  motor.     It  may 
be  almost  perfectly  met  by  the  compound-wound  motor.     It 
is    not    met,  without   the   aid    of   special    mechanism,   by    the 
series-wound  motor. 

361.  Considering   first    the  case  of  a  shunt-wound  motor, 
represented  in   Fig.  165,  the  speed  at  which  the  armature  will 

JB 

run  is  —  revolutions-per-second  (Par.  321),  when  at  no  load,  pro- 
vided that  the  friction  of  the  machine  is  so  small  that  we  may 
safely  neglect  the  drop  of  pressure  in  the  armature  running  light. 
When  the  full-load  current  /  amperes,  passes  through  the 

armature,  the  speed  will  be  reduced  to revolutions-per- 
second,  ry  being  the  armature  resistance  in  ohms. 

Thus  a  particular  shunt-wound,  no-volt  motor  has  an  arma- 
ture resistance  (hot)  of  0.075  ohm,  and  its  full-load  output  is 
9  H.  P.  What  will  be  its  fall  in  speed  between  no  load  and  full 
load,  its  no-load  speed  being  1,395  revolutions-per-minute  or 
23.25  revolutions-per-second? 

Here,  neglecting  the  armature  torque  and  drop  in  pressure 
at  no  load,  e,  the  dynamo  power,  or  volts-per-revolution-per- 

1 10 
second  = =  4.73.     Its  output  at  full  load  being  9  X  746 

=  6,714  watts,  and  its  armature  efficiency,  say,  0.84,  the  arma- 
ture intake  will  be       0     =  7,994  watts  =  72.68  amperes X  no 
o.  04 

volts.     The  full-load  armature  drop  will,  therefore,  be  72.68  x 

0.075  =  5-45  volts,  and  the  full-load  speed —   =   22.1 

4-73 

revolutions-per-second,  approximately,  or  1,326  revolutions- 
per-minute. 

The  drop  in  speed  of  this  motor  between  no  load  and  full  load 
is,  therefore,  69  revolutions-per-minute  ;  or,  approximately 
5  per  cent. 


REGULATION   OF  MOTORS.  283 

362.  If  the  variation  of  speed  due  to  the  drop  in  the  armature 
with  the  full-load  current  is  greater  than  that  which  the  con- 
ditions   of  driving  will   permit,  then  means  may   be   adopted 
to  reduce  the  value  of  ^,  at  full  load  in  the  above  formula,  so 
as  to  increase  the  speed   in  compensation   for   the  necessary 
drop.     This  is  frequently  accomplished  by  inserting  resistance 
in  the  circuit  of  the  field  magnet  so  as  to  reduce  its  M.  M.  F., 
and,  consequently,  the   useful  flux  which  it  sends  through  the 
armature.       A  rheostat  in   the   shunt-field   circuit,    therefore, 
enables  such  regulation  to  be  made  by  hand,  as  will  maintain 
the  speed  of  a  shunt-  motor  constant  under  all  torques  within 
its  full  load.      For  most  commercial  purposes  the  'automatic 
regulation    of  the  shunt  motor  is  sufficiently  close,  the  rheo- 
stat only  being  employed  on  special  occasions.      The  larger 
the  shunt  motor  the  less  the  drop  in  speed  which  is  brought 
about  by  the  full-load  current.     Thus  a  i-H.  P.  shunt  motor 
will  usually  drop  only  10  per  cent,  in  speed  at  full  load,  a  10- 
H.  P.  motor  5  per  cent.,  and  a  loo-H.  P.  motor,  3  per  cent. 

363.  When  a  series  motor  is  operated  on  a  series  circuit,  as 
for  example,  on  a  series-arc  circuit,  some  device  is  necessary 
which  will  regulate  the  speed  of  the  motor.      If  no  such  device 
were  provided,  if  the  starting  torque  of  the  motor  due  to  the 
constant  current  passing  through  it,  exceeded  the  torque  due 
to  load  and  frictions  combined,   the   motor  would  accelerate 
indefinitely  in  its   endeavor   to  oppose   by   C.    E.    M.    F.   the 
passage  of  the  current.     If  the  load  were  of  such  a  nature  that 
the  torque  increased  with  the  speed,  as  in  the  case  of  a  fan, 
the   speed   might  be  automatically  controlled,   but,    since,    in 
driving  machinery,   the  torque  is  nearly  independent  of  the 
speed,    a    controlling    mechanism    becomes    essential.       One 
method   by   which    this    is   accomplished   is    by    rotating   the 
rocker  arm  and  brushes  into  such  a  position  about  the  com- 
mutator, that  the  useful  flux  from  the  constantly  excited  series- 
wound  field  coils,  passing  through  the  armature  coils,  is  virtu- 
ally reduced  by  passing   both  into  and  out  of   the  armature 
coils  when  the  diameter  of   commutation  is  shifted,  thereby 
neutralizing    the     electro-dynamic     force    on   the    windings. 
The    method    corresponds    to    that   adopted    for  varying   the 
E.    M.    F.  of    arc    dynamos,    in    order  to  keep  the     current 


284 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


strength  constant  in   the  circuit,  despite    variations    of   load. 
(Par.  261.) 

Fig.  215,  represents  a  small  series-wound  -J--H.  P.  motor  for 
use  on  series-arc  circuits  and  provided  with  a  hand  regulator 
to  control  the  speed.  The  rocker  arm,  which  supports  the 
brush-holders,  has  a  projection  Pt  to  which  an  insulating 


FIG.  215. — ONE-SIXTH  H.  P.  MOTOR  FOR  ARC  CIRCUITS  WITH  HAND  OR  TREADLE 
REGULATOR,    ROTATING   BRUSHES,    AND   AUTOMATIC    CUT-OUT. 

handle  or  treadle  is  attached.  Under  ordinary  conditions, 
the  spiral  spring  S,  pulls  the  rocker  arm,^  into  the  position 
shown,  so  that  the  brushes  £,  £,  rest  upon  the  commutator  at 
a  diameter  at  right  angles  to  the  diameter  of  neutral  commu- 
tation in  an  ordinary  bipolar  motor,  so  that  the  torque  of  the 
motor  will  be  reduced  to  zero.  By  rotating  the  rocker  arm 
with  handle  or  treadle  against  the  tension  of  the  spring  S,  so 
that  the  projection  P,  occupies  the  position  P',  the  brushes 
are  brought  forward  to  the  position  b\  of  maximum  torque, 
so  that  the  speed  of  the  motor  may  be  controlled. 

In  the  motor  represented  in  Fig.  216,  this  rotation  of  the 
rocker  arm  is  effected  automatically  by  the  aid  of  a  centrifugal 
governor  G,  mounted  at  one  end  of  the  armature  shaft. 


OK 

REGULATION  OF  MOTORS.  285 

When  the  motor  is  started,  by  throwing  it  into  the  series  cir- 
cuit by  a  switch,  the  brushes  are  at  the  diameter  of  neutral 
commutation  or  maximum  torque.  If  the  load  torque  is  not 
too  great  for  the  armature  to  overcome,  the  motor  will 
accelerate  until  the  governor  G,  has  lifted  its  wings  tor  such 
•a  distance  by  centrifugal  force  against  the  tension  of  its 

R 

Q 


FIG.    2l6. — ONE-H.    P.    ARC    MOTOR   WITH    AUTOMATIC    GOVERNOR. 

•spring,  that  the  lever  Z,  following  the  motion  of  the  governor, 
has  pulled  round  the  rocker  arm  and  brushes  to  a  diameter  at 
which  the  torque  of  the  armature  is  equal  to  that  of  the  load. 

364.  In  the  ordinary  motor  the  speed  increases  until  the 
current  strength  /  amperes  passing  the  armature  at  the  ter- 
minal pressure  E  volts,  limits  the  intake,  E  I  watts,  to  the  load 
activity  and  energy  losses  combined.  In  this  motor  the  speed 
increases  until  the  governor  moves  the  brushes  into  such  a 
position  that  the  C.  E.  M.  F.,  E  volts,  limits  the  activity  of  the 
constant  current  7  amperes  to  the  amount  El  watts,  equal  to 
the  load  activity  and  energy  losses.  The  speed  will,  therefore, 
vary  with  the  load  by  a  small  amount  depending  upon  the 
sensibility  of  the  governor. 

Motors  for  series-arc  circuits  are  not  usually  employed 
above  3  H.  P.  Owing  to  the  high  pressure  which  may  exist 


286  ELECTRO-DYNAMIC  MACHINERY. 

upon  their  circuits,   they  may  be  dangerous  to  handle  unless 
precautions  are  taken. 

365.  When  a  series-wound   motor  is  employed  across  con- 
stant-potential mains,  in  the  manner  indicated  in  Fig.  164,  the 
value  of  e,  the  dynamo  power,  or  E.  M.  F.  per-revolution-per- 
second,  being  equal  to  cb  w,   varies  with  the  torque  or  load, 
since  any  change  in  the  current  strength  through  the  armature 
changes  the  M.  M.  F.  of  the  field  magnets,  and,  therefore,  the 
flux  d).     The   tendency   of  a   series   motor   is,    therefore,    to 
reduce  its  speed,   as  the  torque  imposed  upon  the  motor  is 
increased,  and  such  a  motor  would  run,  theoretically,  at  an 
infinite  speed  on  light  load,  if  there  were  no  frictions  in  the 
armature  to  be  overcome.     A  shunt-wound  motor,  therefore, 
tends  to  drop  in  speed  with  load  to  an  extent  proportional  to 
the  drop  of  pressure  in  the  armature.     A  series-wound  motor 
falls  off  in  speed  with   load,   not  only  owing  to  the  drop   of 
pressure  in  the  armature,   but  also  owing  to  the  increase  in 
M.  M.  F.  and  flux. 

366.  A  compound-wound  motor  will,  however,  maintain  its 
speed  practically  constant  under  all  loads,  if  the  series  winding 
on  the  field  coils  be  so  adjusted  that  the  increase  in  current 
strength  through  these  coils  and  the  armature  shall  diminish 
the  M.  M.  F.  of  the  field  magnets  to  the  degree  necessary  to 
compensate  for  the  drop  of  pressure  in  the  armature  winding. 
The  connections  of  such  a  compound-wound    motor  are  the 
same  as  for  the  compound-wound  dynamo  shown  in  Fig.  166. 

367.  Although  a  series-wound  motor  is  unfitted  for  maintain- 
ing a  constant  speed  on  constant-potential  mains  with  variable 
torque,  yet  it  is  possible  to  connect  two  series-wound  machines 
of  the  same  type  and  character  together,  one  acting  as  a  gener- 
ator and  the  other  as  a  motor,  and  to  obtain  a  nearly  constant 
speed  of  the  motor  by  compensatory  changes  in  the  E.  M.  F. 
of  the  generator  automatically  brought  about  by  the  variations 
of  load.     This  case,  however,  can  only  apply  to  a  single  motor 
driven  by  a  single  generator,  and  is,  therefore,  inapplicable  to 
a  system  of  motors  driven  by  a  single  generating  source. 


REGULATION  OF  MOTORS.  287 

368.  Figs.  217  and  218  are  diagrams  taken  from  actual  tests 
of  two  small  5oo-volt,  )^-H.  P.  motors,  of  good  construction  and 
well-known  manufacture,  one  being  a  series-wound  motor  and 


100    200    300    400    500    600    700 

WATTS  INTAKE 

FIG.    217. — TEST    DIAGRAM   OF    A*SHUNT-WOUND   ONE-HALF   H.    P.    MOTOR 
SHOWING   DISTRIBUTION   OF   ACTIVITY. 

the  other  a  shunt-wound  motor.  The  armatures  of  the  two 
machines  and  also  their  field  frames  were  practically  identical, 
the  only  essential  difference  between  the  two  being  in  the  field 


288  ELECTRO-DYNAMIC  MACHINERY. 

winding.  The  weight  of  the  machines  was  105  Ibs.  each,  that 
of  the  armature  nearly  22  Ibs.  The  resistance  of  the  armatures 
was  40  ohms  each,  and  the  resistance  of  the  fields  3,680  ohms 
for  the  shunt-wound,  and  37.5  ohms  for  the  series-wound, 
machine. 

In  these  diagrams,  the  ordinates  represent  the  expenditure 
of  activity  in  the  field  windings,  armature  windings,  frictions 
(including  hysteresis,  eddy  currents,  and  mechanical  frictions), 
and  output  at  the  shaft.  The  abscissas  represent  the  intake 
in  watts.  Thus,  referring  to  Fig.  217  for  the  shunt-wound 
machine,  it  will  be  seen  that  when  delivering  full  load,  or  373 
watts,  the  machine  absorbed  690  watts,  expending  90  in  the 
field  magnets,  as  P  R,  67  watts  in  the  armature  as  72  R,  and 
160  watts  in  total  frictions.  The  commercial  efficiency  of  the 

machine  at  full  load,  was,  therefore,  f42  or  54  per  cent.     The 

690 

speed  of  the  machine  falls  from  29.2  to  25  revolutions-per- 
second,  or  from  1,752  to  1,500  revolutions  per  minute,  a  drop 
of  14.4  per  cent.,  and  this  drop  is  closely  proportional  to  the 
output.  The  highest  commercial  efficiency  reached  was  55  per 
cent,  at  340  watts  output. 

Taking  now  the  series-wound  machine  referred  to  in  Fig.  218, 
it  will  be  observed  that  the  field  loss  is  much  smaller,  particu- 
larly at  light  loads,  owing  to  the  fact  that  it  increases  with  the 
current  strength,  and  practically  disappears  when  the  current 
strength  is  very  small.  Owing  to  this  fact  it  will  be  observed 
that  the  commercial  efficiency  of  this  machine  is  greater 
throughout  than  that  of  the  shunt  machine.  At  a  delivery  of 
340  watts,  the  intake  was  600  watts,  expended  as  follows  :  57 
watts  in  the  magnets,  63  in  the  armature,  and  140  watts  in 
frictions.  It  will  be  seen,  however,  that  the  speed  falls  from 
38.5  to  21.5  revolutions-per-second,  or  from  2,310  to  1,290 
revolutions-per-minute,  a  drop  of  44.2  per  cent.  It  is  clear, 
therefore,  that  a  series-wound  machine  is,  in  small  sizes,  cheaper 
to  construct  than  a  shunt-wound  nfachine,  since  it  employs  only 
a  few  turns  of  coarse  wire  instead  of  many  turns  of  fine  wire 
in  its  field  coils.  It  also  has  a  slightly  higher  efficiency.  It 
also  dispenses  with  the  use  of  a  starting  rheostat  in  the  arma- 
ture, but  has  the  disadvantage  of  possessing  a  much  greater 
variation  in  speed  under  variations  of  load. 


REGULATION  OF  MOTORS. 


289 


369.  As  already  mentioned,  the  condition  of  constant  torque 
and  variable  speed  is  one  which  it  is  much  more  difficult  for 
the  electric  motor  to  meet.  If  it  were  possible  to  vary  the 


700 


600- 


500 


40  400 


80  300 


20200 


i" 


Pfs 

1 

£g2 
Sit 
&3£ 


100 


.200    300    400 

WATTS  I.NTAKB 


500        600        700 


FIG.    2l8. — TEST   DIAGRAM   OF   A   SERIES-WOUND   ONE-HALF    H.    P.    MOTOR 
SHOWING    DISTRIBUTION    OF    ACTIVITY. 

useful  magnetic  flux  through  the  armature  within  wide  limits, 
the  method  of  varying  the  M.  M.  F.  of  the  field  magnets 
would  effect  the  result  desired.  While,  however,  it  is  possible 
to  produce  a  variation  of  speed  in  the  ratio  of  3  to  i, 


290 


ELECTRO-D  YNA MIC  MA  CHINER  Y. 


by  varying  the  M.  M.  F. ;  that  is  to  say,  while  motors  have 
been  constructed,  under  special  conditions,  which  will  run,  say 
at  from  a  maximum  of  900,  to  a  minimum  of  300  revolutions- 
per-minute,  merely  owing  to  variation  in  the  M.  M.  F.  of  their 
fields,  yet  such  a  range  is  only  obtained  with  great  difficulty, 
owing  to  the  fact  that  magnetic  saturation  is  reached  at 
maximum  M.  M.  Fs.  in  the  iron  constituting  the  magnetic 
circuit,  and  that  when  the  field  flux  is  greatly  reduced,  the 
armature  reaction  at  full  load  is  liable  to  be  excessive,  with 
heavy  sparking  at  the  commutator.  The  maximum  range  of 


FIG.   2IQ. — DIAGRAM    SHOWING   ONE   METHOD   OF    SERIES-PARALLEL    FIELD 
EXCITATION    IN    A    STREET-CAR    MOTOR. 


speed  in  an  ordinary  shunt  motor,  brought  about  by  field 
regulation,  is  only  about  25  per  cent,  so  that  a  motor  whose 
maximum  safe  speed  is  1,000  revolutions-per-minute,  can  be 
reduced  to  minimum  of  about  750  revolutions. 

370.  The  M.  M.  F.  of  a  motor  field  may  be  varied  electric- 
ally in  two  ways;  namely,  by  altering  the  current  strength 
through  the  field  coils  as  a  whole,  by  inserting  a  varied  resist- 
ance in  their  circuit;  and  second,  by  altering  the  action  of 
certain  portions  of  the  field  coils  relatively  to  other  portions, 
as,  for  example,  by  changing  them  from  series  to  parallel,  or 
the  reverse.  In  shunt-wound  motors,  the  regulation  is 
usually  effected  by  the  introduction  of  a  field  rheostat.  In 
series-wound  motors  it  is  usually  effected  by  varying  the 
number  or  arrangement  of  the  field  coils.  Thus  the  arrange- 
ment for  connecting  the  field  coils  of  a  particular  form  of 
street-car  motor  is  represented  in  Fig.  219.  It  will  be  seen 
that  there  are  three  coils  on  each  limb  of  the  field,  but  each 


REGULATION  OF  MOTORS. 


291 


pair  is  permanently  connected  as  shown,  so  that  electrically 
there  are  only  three  coils,  A,  B  and  C.  By  the  action  of  the 
controlling  switch,  these  coils  may  be  connected  as  shown  in 
the  diagram. 

In  Position  i,  all  three  coils  are  in  series,  making  the  rela- 
tive M.  M.  F.  3  and  the  relative  resistance  3. 

In  Position  2,  one  coil  is  short  circuited,  making  the  rela- 
tive M.  M.  F.  2  and  the  relative  resistance  2. 

In  Position  3,  two  coils  are  connected  in  parallel,  making 
the  relative  M.  M.  F.  2  and  the  relative  resistance  1.5. 

In  Position  4,  two  coils  only  are  connected  in  parallel,  mak- 
ing the  relative  M.  M.  F.  i  and  the  relative  resistance  0.5. 

In  Position  5,  all  three  coils  are  connected  in  parallel,  mak- 
ing'the  relative  M.  M.  F.  i  and  the  resistance  0.333. 

Fig.  220  represents  the  characteristic  curve  of  a  particular 
motor  of  this  character,  with  the  flux  in  megawebers,  passing 


3.0 

12.5 

52.0 

I 

§1.5 

1 1.0 
10.5 


AMPERE  TURNS  M.M.F. 

FIG.    220.— CURVE  OF   MAGNETIC    FLUX   THROUGH   ARMATURE   IN    RELATION 
TO    M.  M.   F.    OF    FIELD    MAGNETS. 

S 

through  the  armature  with  different  excitations  of  the  field 
magnets,  expressed  in  ampere-turns.  With  the  aid  of  this 
curve  it  is  possible  to  estimate  the  range  of  speed  which  can 
be  obtained  by  connecting  the  coils  in  different  arrangements. 
For  example,  at  half  load  of  7^  H.  P.,  or  say  5,600  watts  out- 
put, and  an  efficiency  of  say  0.8,  the  activity  absorbed  would 


292  ELECTRO-DYNAMIC  MACHINERY. 

be  7,000  watts,  or  14  amperes  at  500  volts  pressure.  There 
are,  approximately,  2,100  turns  in  the  field  coils,  or  700  to 
each  pair,  so  that  with  all  in  series,  the  total  M.  M.  F.  would 
be  14  x  2,100  =  29,400,  which  might  produce  a  flux  of  2.9 
megawebers  through  the  armature.  With  all  the  coils  in 
parallel,  the  M.  M.  F.  would  be  three  times  less  or  9,800,  and 
the  flux  2.12  megawebers.  The  ratio  of  speed,  therefore, 

would  be  -    -  =  1.368,  so  far  as  regards  the  effect  of  change 

in  magnetic  flux  through  the  armature.  In  practice,  the 
speed  would  vary  in  a  somewhat  greater  ratio,  owing  to  the 
influence  of  greater  drop  in  the  field  magnets  when  connected 
in  series  than  when  connected  in  parallel.  We  may  consider, 
therefore,  that  at  light  loads  the  influence  on  the  speed  of 
varying  the  field  coil  connections  is  considerable,  but  at  heavy 
loads  the  influence  is  relatively  small. 

371.  We  have  seen  how  the   speed  of  a  motor  can  be  con- 
trolled within  certain  limits  by  varying  the  magnetic  flux  use- 
fully passing  through  its  armature.     The  same  results  can  be 
effected  by  introducing  resistance  into  the  armature  circuit. 

372.  If  the  constant  torque  imposed  upon  the  motor  is  such  as 
requires  a  current  of  /amperes  to  pass  through  its  armature, 
while  a  given  constant  magnetic  flux  is  produced  by  the  field, 
and  if  E,  be  the  pressure  in  volts  across  the  main  leads,  and  ;-, 
the  resistance  of  the  armature  in  ohms,  the  drop  in  the  armature 
will  be  Ir  volts,  and  the  armature  of  the  motor  must  develop 
that  speed  which  will  produce  a  C.  E.  M.  F.  of  (E  —  I  r)  volts. 
If  it  be  required   to  reduce  this  speed   to  say,  one  half,  then 
the  total  resistance  of  the  armature  circuit  must  be  increased 

rt  -9 

to  R  ohms,  in  such  a  manner   that  E  —  I R  =  -          — ,  so 

that  £  =  -    |"      r .     While  this  plan  is  theoretically  effective, 

it  is  practically  objectionable,  because,  in  the  first  place,  it 
wastes  energy  by  the  introduction  of  the  additional  resistance 
(1?  —  r)  ohms,  the  amount  of  activity  wastefully  expended  in 
such  resistance  being  /*  (R  —  r)  watts.  In  the  second  place, 
a  comparatively  small  accidental  variation  in  the  torque,  which 


REGULATION  OF  MOTORS. 


293 


we  have  hitherto  supposed  constant,  would  effect  a  large 
variation  in  the  speed,  owing  to  the  varying  drop  in  the  added 
resistance.  Again,  a  powerful  motor  requires  a  powerful  cur- 
rent strength  to  be  supplied  to  it,  and  a  large  expenditure  of 
energy  is  necessary  in  order  to  greatly  reduce  its  speed  in  this 


B  B 

FIG.  221. — SYSTEM  OF  PRIME  MOTOR,  GENERATOR,  AND  WORKING  MOTOR 
FOR  CONTROLLING  THE  SPEED  AND  DIRECTION  OF  THE  WORKING  MOTOR. 
UNDER  CONSTANT  TORQUE. 

manner,  requiring  the  use  of  bulky  and  expensive  resistances, 
to  dissipate  the  heat  developed.  For  these  reasons  this 
method  of  maintaining  the  speed  constant  is  seldom  employed. 

373.  It  has  been  found  so  difficult  in  practice  to  vary  the 
speed  of  a  motor  at  constant  torque  between  full  speed  and 
rest,  without  loss  of  efficiency,  that  in  cases  where  complete 
control  is  imperative,  as  in  some  rolling  mills,  where  the 
machinery  has  to  run  occasionally  at  a  definite  very  low  speed, 
and  at  other  times  at  full  speed,  a  method,  which  is  repre- 
sented in  Fig.  221,  has  been  invented  and  applied.  Here  M, 
is  a  shunt-wound  motor,  connected  across  a  pair  of  supply 
mains,  A  A,  B  B,  and,  therefore,  running  at  practically  con- 
stant speed  under  all  conditions  of  use.  The  armature  of  this 
motor  is  connected  directly,  either  by  a  belt  or  by  a  rigid 
coupling,  to  the  armature  of  the  generator  G,  whose  field 
magnets  are  excited  through  a  rh'eostat  R.  The  generator 
armature  consequently  runs  at  a  practically  constant  speed 
under  all  conditions  of  service.  The  E.  M.  F.,  which  this 


294  ELECTRO-DYNAMIC  MACHINERY. 

generator  armature  develops,  depends,  however,  upon  the 
excitation  of  its  field  magnets,  which  is  regulated  by  the 
rheostat  R,  so  that,  when  no  current  passes  through  the 
generator  field  coils,  the  E.  M.  F.  of  its  armature  is  nearly 
zero,  while,  when  full  current  strength  passes  through  the 
field  coils,  the  E.  M.  F.  of  the  generator  is  at  its  maximum. 
The  brushes  of  the  generator  are  directly  connected  with  the 
brushes  of  the  working  motor  m,  whose  field  magnet  is  con- 
stantly excited,  and  the  speed  of  the  armature  m,  will  be  con- 
trolled directly  by  the  E.  M.  F.  of  the  generator  G.  If  the 
generator  is  fully  excited,  the  E.  M.  F.  at  the  terminals  of  the 
motor  m,  will  be  a  maximum,  and  the  speed  of  the  motor  to 
meet  this  E.  M.  F.  with  a  corresponding  C.  E.  M.  F.  will  also  be 
a  maximum,  while  if  the  generator  -has  its  excitation  removed, 
the  armature  of  the  motor  m  may  come  almost  or  quite  to  a 
standstill.  If  necessary,  the  connecting  wires  between  the 
armatures  of  G  and  m,  can  then  be  reversed  so  that  the  direc- 
tion of  m's  rotation  can  be  reversed. 

374.  The  fact  that  this  combination  of  machines  operates 
satisfactorily  without  excessive  sparking  at  the  commutator  of 
the  generator,  often  occasions  some  surprise  to  those  who  are 
accustomed  to  varying  the  field  excitation  of  generators  and 
motors,  under  ordinary  conditions,  since  it  is  known  that,  in 
general,  when  a  generator,  and  particularly  a  motor,  has  its 
field  magnets  considerably  weakened,  a  violent  sparking  is  apt 
to  be  produced  at  the  commutator.      It  is  to  be  remembered, 
however,    in  this  case,   that    the    armature   of   the   weakened 
generator  G,  is  never  permitted  to  send  more  than  the  full- 
load  current  strength,  which  is  required  to  overcome  the  full- 
load    torque,    while   on   the   contrary,  if    this    machine    were 
employed   across    constant-potential    mains    as    a   motor   and 
the   magnetic    flux    through    the    armature   was   considerably 
weakened,  the  current  strength  which  would  pass  through  the 
armature  would  be,  probably,  much  in  excess  of  the  full-load 
current,  with  a  corresponding  tendency  to  produce  excessive 
armature  reaction  and  sparking. 

375.  Although    the    preceding   combination    of    apparatus 
effects  the  desired  result  of  varying  or  reversing  the  speed  of 


REGULATION  OF  MOTORS.  295 

the  motor  at  will,  under  constant  or  even  under  variable  torque, 
within  the  limits  of  full  load,  yet  it  has  the  double  disadvan- 
tage of  requiring  the  installation  of  three  times  the  amount  of 
machinery  which  would  otherwise  be  necessary,  and  of  hav- 
ing a  considerably  reduced  efficiency  of  operation.  If,  for 
example,  the  motor  M,  has  to  be  a  ic-KW  machine,  then  the 
generator  Gt  must  at  least  have  a  capacity  of  10  KW,  and  at 
least  an  equal  capacity  will  have  to  be  given  to  the  prime 
motor  M;  so  that  30  KW  of  machinery  are  installed  where  but 
10  are  directly  brought  into  use.  Again,  if  the  commercial 
efficiency  of  each  machine  were  83  per  cent,  at  full  load,  the 
commercial  efficiency  of  the  combination,  under  full  load, 
would  be,  approximately,  0.83  x  0.83  X  0.83  =  0.572,  so  that 
the  combination  would  have  a  full-load  efficiency  of  57.2  per 
cent.  At  light  loads  the  combination  efficiency  would  be 
still  lower;  for  example,  if  at  half  load  the  efficiency  of  each 
machine  were  75  per  cent.,  the  combination  efficiency  would 
be  42.2  per  cent.  On  the  other  hand,  however,  the  introduc- 
tion of  resistance  into  the  armature  circuit  of  a  motor,  in 
order  to  reduce  its  speed,  would  probably  effect  as  low  or  even 
a  lower  efficiency.  It  is  evident,  therefore,  that  in  this  direc- 
tion the  electric  motor  shows  its  weakest  side. 

376.  The  fourth  condition  of  working;  namely,  under  vari- 
able torque  and  variable  speed,  differs  from  the   last  only  in 
Jhe  variability  of  the  torque.     This  being,  as  we  have   seen, 
the  condition  of  working  with  street-car  motors,  it  is  probably 
one  of  the  most  important  conditions  to  be  met.     It  is  met 
within  the  limits  of  practical  requirements  in  street-car  motors, 
partly  by  controlling   the    field    magnets,   and   partly  by  the 
introduction    of   resistance  into  the    armature  circuits.     This 
resistance  may  be  added  either  through  the  series  windings  of 
the  field  coils,  or  by  the  direct  insertion  of  external  resistance. 
The  problem,  however,   of  controlling  within   full   range  the 
speed   of  a  single   continuous-current    motor,    under  varying 
torque,  with  high  efficiency,  is,  strictly  speaking,  yet  unsolved. 

377.  In  some  cases  two  motors  are  rigidly  coupled  together 
so  that  they  may  have  their  armatures  connected  in  series  or 
in  parallel.     In  the  first  case  they  divide  the  pressure  of  the 


296  ELECTRO-DYNAMIC  MACHINERY. 

C.  E.  M.  F.  between  them,  so  that  their  speed  will  be  a  mini- 
mum under  that  condition.  In  the  second  case  they  each  take 
the  full  pressure,  and  so  yield  the  maximum  speed.  At  slow 
speed,  however,  when  connected  in  series,  it  is  evident  that 
the  activity  of  the  combination  will  be  E  I  watts,  since  each 
machine  can  now  take  /  amperes,  E,  being  the  pressure  be- 
tween the  mains,  in  volts.  At  full  speed,  since  each  armature 
can  take  /amperes,  the  available  activity  will  be  2  El  watts. 
The  combined  torque,  for  the  full-load  current  through  each 
armature,  will  be  the  same  whether  they  are  in  parallel  or  in 
series. 


CHAPTER  XXVIII.         * 

STARTING    AND    REVERSING    OF    MOTORS. 

378.  If  a  series  motor  be  at  rest,  and  be  connected  directly 
across  the  mains,  then  if  the  resistance  of  the  armature  and 
magnet  coils  together  be  R  ohms,  the  current  strength  passing 

£ 

through  the  motor  tends  to  become  -^  amperes,  £,  being  the 

E.  M.  F.  in  volts  at  the  supply  mains.  Thus,  if  a  i-H.  P.  series- 
wound  motor  has  a  resistance  in  the  armature  of  0.5  ohm,  and 
a  resistance  in  the  field  coil  of  0.5  ohm,  the  total  resistance  in 
the  machine  will  be  i  ohm,  so  that  the  first  tendency  is  to 

produce  a  current  strength  of =  no  amperes,  as  soon  as 

the  machine  is  connected  with  the  circuit,  assuming  the  mains 
to  have  a  constant  pressure  of  no  volts,  whereas  the  full-load 
current  strength  of  the  machine  will  be  about  10  amperes.  As 
soon  as  the  armature  has  become  able  to  develop  its  full  speed, 
the  motor  will  generate  such  a  C.  E.  M.  F.  as  will  limit  the 
current  through  it  to  that  required  to  expend  the  energy  it 
wastes  and  delivers.  The  rapidity  with  which  the  armature 
will  reach  its  full  speed  depends  upon  the  load  connected  with 
it,  upon  the  inertia  of  the  armature  and  of  its  load,  as  well  as 
upon  the  current  strength  entering  the  armature.  Moreover, 
owing  to  the  self  induction,  or  inductance,  of  the  field-magnet 
coils,  it  is  impossible  to  develop  the  full  current  strength 
immediately  in  them,  even  assuming  that  the  armature  were 
to  remain  at  rest.  As  soon  as  the  current  excites  the  field 
magnets,  the  flux  they  produce,  passing  through  the  magnetic 
circuit,  develops  in  the  field  coils  a  temporary  C.  E.  M.  F., 
which  has  a  powerful  influence  in  checking  the  first  inrush  of 
current  into  the  armature  during  the  first  half  second  or  second 
of  time.  For  this  reason,  a  series-wound  machine  is  much 
more  safely  started  from  rest  to  full  speed  than  a  shunt- 
wound  machine,  in  which  the 'armature  has  to  be  connected 
directly  across  the  mains. 

297 


298 


ELEC7^RO-D  YNAMIC  MA  CHINEK  Y. 


379.  In  all  except  the  smallest  machines  of  the  shunt-wound 
type,  it  is  necessary  to  insert  some  resistance  in  the  armature 
circuit  when  starting  from  a  state  of  rest,  so  that  the  drop 
produced  in  such  resistance  by  the  starting  current  may  limit 
the  amount  of  current  passing  through  the  armature.  For  this 
purpose  special  rheostats,  called  starting  rheostats,  are  inserted 
in  the  armature  circuit.  Since  they  are  only  intended  to  carry 
the  current  during  the  time  that  the  motor  is  coming  up  to 
speed,  they  are  not  usually  designed  to  carry  the  full  current 
strength  of  the  motor  indefinitely,  and,  therefore,  a  starting 
rheostat  should  never  be  maintained  constantly  in  circuit. 
Fig.  222  represents  a  form  of  starting  rheostat  employed  with 
shunt-wound  motors.  Here  a  number  of  coils  or  spirals  of 


FIG.    222. — STARTING    RHEOSTAT. 

galvanized  iron  wire,  are  mounted  in  a  fire-proof  frame  under  a 
cover  of  slate  or  composition,  on  which  a  number  of  contacts 
are  arranged  in  a  circle.  Fig.  223  represents  the  manner  in 
which  such  a  rheostat  is  connected  in  the  armature  circuit. 

380.  If  it  becomes  necessary,  as  we  have  shown,  to  insert 
resistance  into  the  circuit  of  a  shunt-wound  motor  armature, 
in  order  to  start  it  from  rest,  it  is  still  more  necessary  to  insert 
resistance  into  the  armature  circuit,  in  order  suddenly  to 
reverse  its  direction  of  motion.  When  the  armature  terminals 
of  a  shunt-wound  motor  are  suddenly  reversed,  relatively  to  the 
mains,  while  the  field  magnet  coils  remain  permanently  excited, 


STARTING  AND   REVERSING   OF  MOTORS. 


2  99 


the  E.  M.  F.  of  the  armature  due  to  its  speed,  which  was, 
before  the  reversal,  a  C.  E.  M.  F.,  tending  to  check  the  passage 
of  current  strength  through  its  windings,  becomes  now  a  driv- 
ing E.  M.  F.,  tending  to  increase  the  current  strength  passing 
through  it  from  the  mains.  The  effect  of  a  sudden  reversal  in 
a  shunt-wound  motor  armature  is,  therefore,  practically  equiva- 
lent to  suddenly  throwing  the  armature  across  a  pair  of  mains 
having  double  the  pressure  of  those  actually  employed,  and 


FIELD  COILS 
FIG.    223. — CONNECTIONS   OF    STARTING   RHEOSTAT   WITH    SHUNT   MOTOR. 


with  the  attending  consequences  of  an  enormous  overload  of 
current  strength,  which  first  checks,  and  then  reverses,  the 
direction  of  armature  rotation. 


381.  Various  devices  are  employed  for  preventing  a  motor 
armature  from  being  injured  by  the  sudden  reversal  of  its 
terminals  with  the  mains.  At  the  time  when  armatures  were 
almost  all  of  the  smooth-core  type,  damage  was  frequently  done 
by  shearing  the  wires  off  the  armature  core  under  the  very  heavy 


3oo 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


FIG.    224. — FORM    OF    AUTOMATIC    SWITCH. 

electro-magnetic  stresses  thus  brought  to  bear  upon  them  dur- 
ing rotation.  When  toothed-core  armatures  became  generally 
used  this  danger  practically  disappeared,  but  the  danger  of 
damaging  either  the  insulation  of  the  wires,  or 'the  mechanical 
framework  of  the  armature,  or  of  burning  out  some  of  the  con- 


STARTING   AND  REVERSING   OF  MOTORS. 


301 


ductors,  still  remains.  A  starting  coil  is  frequently  employed 
with  street-car  motors  which  consists  of  a  coil  of  strip-iron 
conductor,  having  a  hollow  interior,  so  that  it  contains  a  large 


UWWWWVbl''" 


MO  TO* 


FIG.    225. — CONNECTIONS   FOR   AUTOMATIC    SAFETY    SWITCH    AND    STARTING 

RHEOSTAT. 

magnetic  flux  when  excited.  The  C.  E.  M.  F.  suddenly 
developed  from  such  a  coil,  on  being  magnetized,  is  sufficiently 
great,  to  check,  for  the  moment,  the  first  rush  of  current,  and 
such  a  coil  may  be  called  an  inductance  coil. 


382.  Fig.  224,  represents  the  form,  and  Fig.  225,  the  diagram- 
matic connections  of  a  particular  automatic  switch  and  starting 


302  ELECTRO-DYNAMIC  MACHINERY. 

rheostat  sometimes  employed  with  large  motors.  The  larger 
the  motor  the  more  expensive  does  any  accident  become  which 
may  happen  to  its  armature,  and  the  more  economical  it 
becomes  to  take  precautions  against  such  accidents.  Referring 
to  the  figures,  it  will  be  seen  that  the  mains  or  line  wires  are 
connected  directly  to  two  circular  contact  segments  S,  S, 
through  the  coils  of  a  relay  magnet  JZ.  When  the  handle  H\ 
is  in  such  a  position  that  the  two  contact  bars  B,  B,  rest  in  the 
intermediate  position,  they  lie  out  of  contact  with  the  seg- 
ments, and  the  current  is  then  entirely  cut  off  the  motor.  A 
powerful  spring,  wound  about  the  axis  on  which  the  handle  Jf, 
moves,  tends  to  bring  the  handle  and  the  bars  B,  B^  back  to 
this  zero  or  ''off"  position.  If  the  handle  is  pressed  forward 
in  the  clockwise  direction  against  the  pressure  of  its  spring, 
the  line  wires  are  connected  with  the  armature  through  the 
resistance  coils  r,  r,  r,  which  are  wound  upon  spools  of  insulat- 
ing and  non-inflammable  material  within  the  box,  and  also 
through  the  field  coils  of  the  motor.  When  the  handle  is 
pushed  completely  around  to  the  "on  "  position,  the  extra  re- 
sistances are  cut  out  of  the  armature  circuit  and  the  armature 
thus  becomes  enabled  to  run  at  full  speed.  In  this  position 
the  handle  is  prevented  from  returning  to  zero  and  is  kept  in 
place  by  the  detent  magnet  Z>,  excited  by  the  current  passing 
through  the  field  coils.  If  the  circuit  of  the  field  coils  should 
accidentally  become  broken,  the  magnet  Z>,  will  release  its 
armature,  which  will  release  the  detent,  which  will  allow  the 
handle  H,  with  its  contact  bars  B,  B,  to  return  to  the  "  off  " 
position,  under  the  action  of  the  spiral  spring;  or,  should  the 
armature  current  become  excessively  strong,  thereby  endanger- 
ing the  armature,  the  relay  magnet  will  attract  its  armature, 
which  will  thereby  short-circuit  the  detent  magnet,  and  the 
same  result  will  follow.  The  armature  will,  therefore,  be 
stopped  by  any  overload,  and  will  be  cut  out  of  circuit  by  any 
accidental  cessation  of  the  current  in  the  field.  By  means  of  a 
push-button  circuit,  the  armature  can  be  brought  to  rest,  by 
pressing  a  push  button  placed  at  any  distance  from  the 
machine. 

383.  All  the  phenomena  of  armature  reaction  which  we  have 
traced  in  connection  with  dynamos  in  Pars.  198  to  223  are  pre- 


STARTING  AND  REVERSING   OF  MOTORS,  303 

sented  by  motors,  with  the  exception  that  the  direction  of  the 
M.  M.  F.  of  the  armature,  relatively  to  the  field  magnets,  is 
reversed;  that  is  to  say,  a  motor  runs  so  that  the  magnetic 
flux  produced  by  its  armature  tends  to  pass  through  the  pole 
which  the  armature  approaches;  /.  <?.,  the  leading  pole,  instead 
of  the  trailing  pole,  or  that  from  which  it  is  forced  in  the 
dynamo.  With  this  exception  all  the  effects  of  sparking  and 
cross-magnetization  present  themselves  equally  in  motors  as  in 
dynamos.  The  diameter  of  commutation  in  a  generator  has  to 
be  advanced  in  order  to  obtain  a  sparkless  position;  in  other 
words,  a  lead  has  to  be  given  to  the  brushes,  while  in  a  motor 
the  diameter  of  commutation  has  to  be  retrograded  to  arrive  at 
the  same  result;  in  other  words,  a  lag  has  to  be  given  to  the 
brushes. 

384.  In  order  to  reverse  the  direction  of  rotation  of  a  motor, 
a  single  rule  has  to  be  borne  in  mind;  namely,  the  M.  M.  F. 
either  of  the  field  or  of  the  armature  must  be  reversed.     If 
the  M.  M.  F.  of  both   field   and    armature   be   simultaneously 
reversed,   the    direction    of   rotation    of   the    motors    remains 
unaltered. 

385.  Fig.  226  is  a  complete   diagram  showing  the  relations 
which  exist  between  the  direction  of  rotation  and  the  direction 
of  current  in   the  field  and  armature   of  different  machines. 
The  horizontal  row  on  the  top   represents  separately-excited 
machines;  the  next  lower  row,  shunt-wound  machines,  and  the 
lowest    horizontal    row,   series-wound    machines.       The.  first 
vertical  column,    No.  I,  on   the   right,    represents   generators. 
Column  II,  next  in  order  to  the  left,   represents  the  action  of 
these  machines  as  motors,  when  mounted   in  connection  with 
the  mains,  but  not  supplied  with   sufficient  driving  power  to 
maintain  the  machines  as  generators.     Column  III  represents 
the  effect  of  reversing  the  connection  of  the  armature  when 
the  machine  is  acting  as  a  motor.     Column  IV  represents  the 
effect  of  reversing  the  field  connections  instead  of  the  con- 
nections of  the  armature.      Column  V  represents  the  effect  of 
reversing  both  field  and  armature  connections,  which  is  equiv- 
alent to  reversing  the  entire  machine  relatively  to  the  mains. 
The  large  arrow  on   the  field   coil  represents  the  direction  of 


3°4 


ELECTRO-DYNAMIC  MACHINERY. 


the  M.  M.  F.,  or  of  flux  through  the  field.  The  large  arrow 
on  the  armature  represents  the  direction  of  the  M.  M.  F.  in 
the  armature,  due  to  the  current.  The  small  arrow  in  the 
•centre  of  the  armature  represents  the  direction  of  the  arma- 


ture E.  M.  F.,  relatively  to  the  circuit,  and  the  curved  arrow, 
outside  the  armature,  represents  the  direction  of  rotation  of 
the  armature. 


386.  Referring   to   the    line    or    row    of  separately-excited 
machines,  in  Column  I,  each  machine  appears  as  a  generator, 


STARTING  AND   REVERSING   OF  MOTORS.  305 

rotated  by  the  driving  belt  in  the  direction  of  the  curved 
.arrow.  The  E.  M.  F.  of  the  armature  is  in  the  direction  of 
the  current  through  the  armature,  and  the  mains  are  supplied 
with  current  from  the  brushes,  as  shown.  If  the  driving  belt 
be  suddenly  thrown  off  the  armature  pulley,  the  machine  will 
run  for  a  few  moments  by  its  inertia,  still  supplying  current  to 
the  mains,  until  the  power  so  expended  has  absorbed  the  sur- 
plus energy  of  motion  of  the  armature,  when  the  speed  and 
E.  M.  F.  of  the  armature  will  diminish,  until  the  E.  M.  F.  is 
exactly  equal  to  that  between  the  mains,  which  are  assumed  to 
be  maintained  at  a  constant  difference  of  potential  by  another 
source  of  supply.  At  this  moment  there  will  be  no  current 
through  the  armature.  If  there  were  no  friction  in  the  arma- 
ture, this  condition  might  be  retained  indefinitely,  but  since 
every  machine  must  expend  energy  against  frictions,  the  speed 
of  the  armature  continues  to  slacken,  and  the  E.  M.  F.  in  the 
armature  falls  below  that  in  the  mains.  Current  will  then  pass 
back  from  the  mains  through  the  armature,  as  shown  in  Column 
II,  reversing  the  M.  M.  F.  of  the  armature,  but  maintaining 
the  same  direction  of  rotation.  The  machine  is  now  rotated 
as  a  motor,  absorbing  energy  from  the  mains,  and  the  E.  M.  F. 
of  the  armature  is  now  a  C.  E.  M.  F.,  as  shown  by  the  opposi- 
tion between  the  directions  of  the  small  arrow  in  the  centre  of 
the  armature,  and  the  arrows  representing  the  direction  of 
current  through  the  armature.  Consequently,  a  separately- 
excited  machine  runs  in  the  same  direction  as  generator  or 
motor,  if  no  change  is  made  in  the  armature  or  field  connec- 
tions. If  the  armature  connections  be  reversed,  as  represented 
in  Column  III,  or  if  the  field  connections  be  reversed,  as  rep- 
resented in  Column  IV,  the  direction  of  rotation  of  the  arma- 
ture is  reversed;  but,  if  both  field  and  armature  connections  be 
reversed,  as  in  Column  V,  the  original  direction  of  rotation  is 
retained. 

387.  'In  the  shunt-wound  machines,  represented  in  the  second 
row,  practically  the  same  conditions  are  observed  to  follow; 
namely,  if  the  driving  belt  be  thrown  off  the  pulley  of  the 
machine  acting  as  a  generator,  when  connected  to  constant- 
potential  mains,  current  will  pass  through  the  armature  in  the 
opposite  direction  to  that  which  passes  when  the  machine  is  a 


306  ELECTRO-DYNAMIC  MACHINERY. 

generator,  thus  reversing  the  M.  M.  F.  of  the  armature,  but 
maintaining  the  direction  of  rotation.  Reversing  either  the 
field  or  the  armature,  reverses  the  direction  of  rotation,  but 
reversing  the  entire  machine;  /'.  e.,  both  field  and  armature, 
has  no  effect  upon  the  direction  of  rotation. 

388.  The  third  row;  viz.,  that  of  series-wound  machines,  dif- 
fers, however,  essentially  from  the  foregoing.     Here,  it  will  be 
observed,  that  if  the  belt  be  thrown  off  the  generator,  as  soon  as 
the  E.  M.  F.  of  the  armature  is  brought  down  to  that  existing 
between  the  mains,  no  current  passes  through  the  mains  and 
the  field  magnets  lose   their   excitation.     It  will  follow  from 
this  that  the.E.    M.  F.   of  the  armature  will  very  rapidly  dis- 
appear, and  a  large  rush  of  current  will  pass  through  the  arma- 
ture from  the  mains,  reversing  the   direction,  not  only  of  the 
armature  M.  M.  F.,  but  also  of  the  field  M.  M.  F.,  so  that  the 
machine  is  first  brought  to  a  standstill,  and  then  rotated  in  the 
opposite  direction.     It  is  clear,  therefore,  from  this  considera- 
tion, why  series-wound  machines  are  never  employed  as  inde- 
pendent units,  in  parallel,  for  supplying  a  system  of  mains;  for, 
if  by  any  acccident  the  engine  driving  a  series-wound  generator 
failed  to  maintain  the  E.  M.  F.  of  its  armature  above  that  of 
the  mains,  the  machine  would  become  a  short  circuit  upon  the 
mains,  and  an  enormous  rush  of  current,  with  a  correspond- 
ingly violent  mechanical  effort,  would  be  brought  to  bear  upon 
the  machine,    tending    to    reverse   its    motion  and  drive  the 
engine  backward. 

389.  If  the  series-wound  machine  be  considered  as  running 
in  the  direction  represented  in  Column  II,  and  the  armature 
connections  are  then  reversed,  or  the  field  magnet  connections 
reversed,  as  in  Columns  III  and  IV,  the  direction   of  rotation 
of  the  armature  will  be   reversed,  or  restored  to  the  direction 
of  rotation  as  a  generator  ;  while,  if  both  field  and  armature 
be  reversed,  as  shown  in   Column  V,  the  direction  of  rotation 
will  be  the  same  as  in  Column  II. 

390.  It   is   evident,   therefore,    from   an  inspection   of   the 
diagram,  that  it  is  only  necessary  either  to  reverse  the  direc- 
tion of  the  M.  M.  F.  in  the  armature  or  in  the  field,  to  reverse 


STARTING  AND  REVERSING   OF  MOTORS.  307 

the  direction  of  rotation  of  the  motor,  and  that  the  relative 
direction  of  the  M.  M.  F.  in  field  and  armature  is  opposite  in 
a  motor  to  what  it  is  in  the  same  machine  as  a  generator. 
For  this  reason  the  leading  pole-pieces  of  a  machine,  when 
operating  as  a  generator,  and  the  following  pole-pieces  when 
operating  as  a  motor  are  weakened  by  armature  reaction. 

391.  In  practice,  it  is  always  the  connections  of  the  armature 
of  a  machine  which  are  reversed,  in  order  suddenly  to  reverse 
the  direction  of  its  rotation,  for  the  reason  that  the  inductance 
of  the  armature  being  usually  much  less  than  that  of  the  field, 
the  change  is  more  readily  effected,  and  with  less  danger  of 
injuring  the   machine  by  an  excessive  rise  of  pressure.     On 
the  other  hand,  if  the  machine  be  brought   to  rest  and  dis- 
connected from   the  circuit,  it  may  be  just  as   convenient  to 
reverse  the   field  magnet  connections  as  the  armature  connec- 
tions, in  order  to  effect  a  reversal  of  rotary  direction   when 
the  machine  is  next  started. 

392.  In  all  cases  it  has  to  be  remembered  that  it  is  dangerous 
to  break  the  circuit  of  the  field  magnets  of  a  motor  when  in 
operation,  not  only  because  by  so  doing  the  M.  M.  F.  of  the 
field  is  almost  entirely  removed,  and  thereby  the  armature  is 
unable  to  develop  a  C.  E.  M.  F.,  becoming  practically  a  short 
circuit  on  the  mains;  but  also,  because  the  powerful  E.  M.  F. 
generated  in  the  field  coils  by  self-induction,  when  their  circuit 
is  interrupted,    may  find    a  discharge  through    the   armature 
insulation,  in  such  a  manner  as  to  pierce   the  same  and  per- 
manently injure   the  armature.     The   same  remarks  apply  to 
the  operation   of  machines  as   generators.     The  field    magnet 
connections  should  always  be  the  first  to  be  completed,  and  the 
last  to  be  interrupted,  when  the  machine  is  operated  in  either 
capacity. 

393.  In  some  cases,  it  is  possible  for  the  M.  M.  F.  of  the 
armature   to  overcome   that  of  the  field  magnets,  and  actually 
to  reverse  the  direction  of  magnetic  flux   through  the   mag- 
netic circuit  of  the  machine.      For  example,  if  a  shunt-wound 
machine  be   operating  alone,  and  supplying  a  system  of  mains, 
it  is  possible  for  a  very  powerful  current  passing  through  the 


ELECTRO-DYNAMIC  MACHINERY. 

armature  to  produce  such  an  armature  reaction  as  shall  effect 
a  large  C.  M.  M.  F.  in  the  magnetic  circuit  of  the  machine,  and 
so  reverse  the  magnetic  flux  in  the  circuit.  As  soon  as  this  is 
effected,  the  E.  M.  F.  of  the  armature  will  be  extinguished  and 
the  machine  will  cease  to  send  a  current.  This  effect  is 
distinct  from  the  tendency  of  shunt-wound  generators  to  lower 
their  E.  M.  F.  under  heavy  loads,  by  reason  of  the  drop  in  the 
armature,  and  its  effect  upon  the  excitation  of  the  field  mag- 
nets. It  can  only  happen  when  the  brushes  of  the  machine 
are  given  a  considerable  lead;  for,  if  the  brushes  be  maintained 
at  the  neutral  point  midway  between  the  poles,  it  will  be 
impossible  for  the  armature  reaction  to  produce  a  dangerously 
large  C.  M.  M.  F.  in  the  main  magnetic  circuit.  Such  acci- 
dents have,  however,  taken  place  in  central  stations  with  types 
of  generator  in  which  the  armature  reaction  and  lead  of  the 
brushes  at  full  load  is  considerable.  For  this  reason  it  is 
preferable  to  excite  the  field  magnets  of  large  central  station- 
generators  from  independent  machines,  when  possible. 

394.  In  motors,  which  are  required  to  have  their  direction 
reversed,  it  is  necessary  that  the  brushes  shall  rest  upon  the 
commutator  in  such  a  position  as  shall  permit  of  this  reversal 
of  direction  without  danger.  Carbon  brushes  are  employed 
with  practically  all  5oo-volt  generators  and  motors,  and  with 
such  machines  for  lower  pressures  as  will  permit  of  the  passage 
of  the  full-load  current  through  the  carbon  brushes  without 
dangerously  overheating  them.  Their  advantage  is  that  they 
wear  evenly,  lubricate  the  surface  of  the  commutator,  and  are 
readily  replaced.  Their  only  disadvantage  is  their  high 
resistivity,  and  the  noise  they  are  apt  to  make  if  the  commuta- 
tor surface  is  not  perfectly  uniform. 


CHAPTER   XXIX. 

METER-MOTORS. 

395.  It  sometimes  becomes   necessary  to   design  a  motor, 
whose  speed    shall  be  proportional   to   the  current  strength 
passing  through   it.     This   problem  arises   in   devising  motor- 
meters  for  determining  the  quantity  of  electricity  supplied  to 
a  customer  from  a  pair  of  constant-potential  mains,  as  in  elec- 
tric lighting.     The  motors  employed  for  this  purpose  are  of 
very    small    sizes.     We    propose    to    consider   the    conditions 
under  which  the  speed  of  the  motor  shall  be  proportional  to 
the  driving  current  strength. 

396.  Fig.  227  represents  a  pair  of  constant-potential  mains, 
marked  -f-  and  — ,  with  a  small  motor  J/",  designed  to  measure 
the  current  strength  supplied  to  the  incandescent  lamps,  L  L, 
with  which  it  is  connected  in  series.     It  is  evident  that  the 
current  which  passes   through  the  motor  armature  will  vary 
directly  with  the  number  of  lamps  which  are  turned  on.     The 
connections  of  the  motor  field  magnets  are  not  shown.      These 
magnets  may  be  constantly  excited  from  the  mains,  thus  virtu- 
ally constituting   a    separately-excited  field ;   or,  a  permanent 
magnet  field   may  be   employed   for  this  purpose.     In   either 
case  the  strength  of  the  field  flux  may  be  considered  as  inde- 
pendent of  the  load. 

397.  We^know  that  (Par.  313)  if  /,   be  the  current  strength 
passing  through  the  armature  in  amperes,  #,  the  field  flux,  in 
webers,    usefully  passing  through  the  armature,   and   w,    the 
number  of  turns   on  the  armature,   counted  once  completely 
around;  the  torque-per-ampere,  which  will  be  exerted  about 
the  armature  shaft  will  be 

#  w 
f  = cm. -dynes  per  ampere. 

If  no  load  except  friction  were  imposed  upon  the  armature, 
that  is  to  say,  if  it  were  free  to  run  without  retarding  torquer 

309 


3io 


ELECTRO-D  YNAMIC  MA  CHINER  Y. 


beyond  a  frictional  torque  of  f  cm. -dynes,  due  to  mechanical 
and  electric  frictions,  then  the  speed  which  the  motor  would 
attain,  as  soon  as  the  first  lamp  was  turned  on,  would  be  very 
great,  assuming  that  the  torque  /  rt  was  sufficient  to  start  the 
motor;  for,  the  friction  /,  would  be  practically  constant  at  all 
speeds,  and  if  /  T,  be  greater  than  f,  the  accelerating  force 
being  greater  than  the  retarding  forces,  will  continually 
increase  the  speed  of  the  motor  until  the  C.  E.  M.  F.  of  the 
armature  reduces  the  current  strength  to  that  which  is  needed 
to  exactly  neutralize  the  retarding  torque.  Such  a  small 
motor,  therefore,  if  unloaded,  would  tend  to  run  at  a  very 


-O- 


FIG   227. — MOTOR   ARMATURE   IN   CIRCUIT   WITH    INCANDESCENT   LAMPS. 

high  speed  and  to  reduce  the  pressure  at  the  terminals  of  the 
lamp. 

398.  It  is  also  evident  that  the  resistance  of  the  armature 
must  be  sufficiently  small,  in  order  that  the  drop  and  C.  E.  M.  F. 
in  the  armature,  produced  by  the  full-load  current,  shall  not 
be  greater  than  say  one  per  cent,  of  the  total  pressure  at  the 
mains.  Let  us  assume  that  we  are  able  to  impose  a  load  or 
torque  upon  the  motor  proportional  to  its  speed.  If  #,  be  the 
number  of  revolutions-per-second  made  by  the  motor,  r,  the 
load  torque  in  cm. -dynes  will  then  be  r  —  a  n,  where  #,  is  a 
constant  quantity.  Under  these  conditions,  the  speed  which 
the  motor  will  attain  will  be  determined  by  the  equality  of  the 
driving  and  resisting  torques  or  /  t  =  an  -\-  f.  From  which 

n  =   — —  revolutions  per  second  = — . 

a  a          a 


.   METER-MOTORS.  311 

399.  For  example,  suppose  a  small  motor  to  be  connected 
as  shown  in  Fig.  227,  in  circuit  with  20  incandescent  lamps, 
each  taking  one  half  ampere  from  a  pair  of  mains  supplied  with 
no  volts  pressure.  The  full-load  current  will  be  10  amperes, 
and,  if  the  resistance  of  the  armature  be  o.  i  ohm,  the  drop 
of  pressure  in  the  armature  at  full  load  will  be  i  volt.  If 
the  torque  r,  of  the  motor  be  200  centimetre-grammes,  or, 
approximately,  200,000  centimetre-dynes  per  ampere  of  cur- 
rent, also  if  the  torque  due  to  frictions  be  75  centimetre- 
grammes,  or,  approximately,  75,000  centimetre-dynes,  and  the 
torque  due  to  load  be  120  centimetre-grammes,  or,  approxi- 
mately, 120,000  centimetre-dynes-per-revolution-per-second, 
then,  if  one  lamp  were  turned  on,  the  current  through  the 
armature  would  be  0.5  ampere.  The  starting  torque  would  be 
100  centimetre-grammes,  the  resisting  torque  of  friction,  75 
centimetre-grammes,  and  the  motor  would  therefore  start 
under  a  resultant  torque  of  25  centimetre-grammes.  It  would 
accelerate  until  a  speed  of  0.208  revolution-per-second  was 
attained,  when  the  resisting  load  torque  would  be  o.  208  x 
1 20  =25  centimetre-grammes.  Proceeding  in  this  way,  we 
can  determine  what  the  speed  of  the  motor  would  be  with  any 
current  strength  as  follows: 


Current 

Moving-  Torque 

Resisting 
Friction 

Torque 
Speed 

Speed  of 
motor 

Speed 
per  lamp 

Lamps. 

amperes. 

cm.  -grammes. 

cm.-gms. 

cm.-gnts. 

rv.  per  s. 

rv.  per  s. 

I 

0-5 

100 

75 

25 

0.21 

O.2I 

2 

1.0 

2OO 

75 

125 

1.04 

0.52 

4 

2.0 

400 

75 

325 

2.71 

0677 

6 

3-0 

600 

75 

525 

4.375 

0.729 

8 

4.0 

800 

75 

725 

6.04 

0.755 

10 

5.o 

1,000 

75 

925 

7.71 

0.771 

12 

6.0 

1,200 

75 

1,125 

9-375 

0.781 

14 

7.0 

1,400 

75 

1,325 

.  11.04 

0.789 

16 

8.0 

1,  6OO 

75 

1,525 

12.71 

0.794 

18 

9.0 

1,  800 

75 

1,725 

14.375 

0.799 

20 

10.0 

2,000 

75 

1,925 

16.04 

0.802 

Here   a  =  120,900  r  =  200, ooo/  =  75,000,    so    that    with 

10  X  200,000  X  75,ooo 

z  =  20,  n  =  ~  -    i  =  6.04. 

120,000 

400.  It   will   be   observed    that,   after   the   first   two  lamps 
have   been    lighted,    the   speed   of   the   motor  is   nearly   pro- 


312  ELECTRO-DYNAMIC  MACHINERY. 

portional  to  the  number  of  lamps,  and,  therefore,  the  total 
number  of  revolutions 'of  a  motor  armature  in  a  given  time, 
will  be  an  approximate  measure  of  the  total  quantity  of  elec- 
tricity supplied  through  the  meter  in  coulombs,  or  in  ampere- 
hours. 

In  order  that  the  error,  introduced  into  the  indications  of 
the  meter,  by  constant  friction  of  the  armature,  shall  be  as 
small  as  possible,  it  is  important  that  the  constant  torque-per- 
revolution-per-second  shall  be  as  great  as  possible,  relatively 

to  the  friction,  or  that  —  shall  be  a  small  fraction. 
a  , 

401.  In  practice  it  would  be  very  difficult  to  arrange  a  motor 
of  this  kind,  having  its  armature  placed  directly  in  the  main 
circuit  of  the  lamps,  for  the  reason  that  if  the  brushes  were 
sufficiently  fine  to  permit  the  friction  of  the  armature  to 
become  negligibly  small,  any  accidental  short-circuit, occurring 
between  the  lamp-leads,  would  probably  destroy  the  brushes, 
or  the  armature,  or  both.  .The  problem  has,  however,  been 
successfully  met  in  practice  by  making  the  armature  in  this 
case  the  fixed  element  of  the  motor,  and  the  field  magnet  the 
moving  element. 

Fig.  228  represents  a  well-known  type  of  meter,  in  which  the 
current  to  be  measured  passes  through  the  stationary  element 
of  the  field  coils  F,  F,  while  the  moving  element,  or  armature 
Mt  is  permanently  magnetized  by  a  feeble  current  passing 
through  a  comparatively  high  resistance,  wound  on  a  frame  at 
the  back  of  the  instrument  and  kept  in  circuit  with  the  mains. 
The  armature  M,  receives  its  current  through  the  delicate 
brushes  ^,  which  rest  on  opposite  sides  of  a  small  silver  com- 
mutator c.  No  iron  is  employed  in  either  the  field  or  armature 
of  the  apparatus.  The. vertical  shaft  of  the  armature  M,  is 
geared  directly  with  a  dial-recording  mechanism  similar  to  that 
of  a  gas  meter.  In  order  to  apply  a  load  torque  proportioned 
to  the  speed,  a  disc  of  copper  Dt  is  mounted  horizontally  upon 
the  vertical  armature  axis,  so  as  to  rotate  between  the  poles 
of  the  three  permanent  magnets  P,  P,  P,  as  shown.  When 
the  disc  is  at  rest  there  is  no  retarding  torque  other  than  a 
small  mechanical  friction  due  to  the  brushes  resting  on  the 
commutator  and  the  weight  of  the  armature  in  its  bearings. 


ME  TER-MO  TORS. 


313 


As  soon  as  the  disc  is  set  in  motion  by  the  rotation  of  the 
armature,  eddy  currents  are  produced  in  its  substance  by  the 
dynamo  action  of  the  permanent  magnets  upon  it,  and  a  re- 
tarding torque  is  set  up  between  the  disc  and  these  magnets. 
At  all  ordinary  speeds  this  torque  is  proportional  to  the  rate 
of  rotation,  thus  complying  with  the  requirements  of  the  motor 
as  a  meter. 

402.  The  armature  of  the  motor  represented  in  Fig.  227  is 


FIG.    228. — WATTMETER. 


only  capable  of  acting  as  a  coulomb  meter,  or  ampere-hour  meter, 
but  the  apparatus  shown  in  Fig.  228,  while  acting  as  an  ampere- 
hour  meter  on  constant  potential  mains,  also  operates  as  a 
watt-meter,  in  cases  where  the  pressure  between  the  mains  is 
not  constant;  for,  all  variations  in  the  pressure  will  also 
increase  in  direct  proportion  the  useful  flux  #,  linked  with 
field  and  armature,  and  so  the  speed  of  the  armature  will  be 
accelerated  and  retarded  in  proportion  to  the  pressure,  as  well 
as  in  proportion  to  the  current  strength. 


314 


ELECTRO-D  Y NAM  1C  MA  CHINER  Y, 


403.  No  law  of  retarding  torque,  other  than  a  torque  pro- 
portional  to  the  speed,  can  give  a  rate  of  revolution  in  the 
armature  proportional  to  the  current  strength  passing  through 
it,  when   the  field  flux   $  is  constant.     If,   however,  the  field 
magnets  be  in  series  with  the  armature,  so  that  <P  increases 
with  the  load,  it  is  possible  for  an  instrument  of  this  character 
to  register  fairly  accurately,  even  although  the  load  torque  is 
not  proportional  to  the  speed.     In  such  cases,   however,  the 
results  can  only  be  approximate,   since  the  hysteresis  in  the 
magnetic  circuit  of  the   field  will   bring  about  a  complicated 
relation  between  load  and  flux. 

404.  Another  problem  which  sometimes  arises,  is  to  design 
a  motor  whose  speed  shall  be  proportional  to  the  pressure  in 


FIG.    229.  —  MOTOR    ARMATURE    SHUNTED    AND    IN    CIRCUIT    WITH    INCANDES- 

CENT  LAMPS. 

volts  at  its  terminals.  This  problem  presents  itself  in  motor- 
meters  having  an  armature  which,  instead  of  being  inserted 
directly  in  the  lamp  circuit,  is  shunted  by  a  constant  small 
resistance  r.  A  motor-meter  of  this  type  is  shown  in  Fig.  229. 
Here  the  danger  of  burning  out  the  armature  by  an  accidental 
overload  is  not  nearly  so  great,  since  the  pressure  at  the  arma- 
ture terminals  can  never  exceed  that  of  the  drop  in  the  shunt 
resistance  r.  If  /,  be  the  total  current  strength  in  amperes 
passing  through  the  lamps,  and  e,  the  dynamo  power  of 
the  armature,  in  volts-per-revolution-per-second,  the  current 
strength  passing  through  the  armature  will  be 


(i—i.)  r  —  n 

'  =  -    - 


i  r  X  n  e 

amperes'  = 


ME  TER-MO  7VRS. 


315 


where  R  is  the  resistance  of  the  motor  armature  in  ohms,  and 
the  driving  torque  will  be  il  r  cm. -dynes. 

If  the  frictional  torque  /,  centimetre-dynes,  be  assumed 
constant,  the  speed  of  the  motor  will  be  determined  by  the 
relation  t\  T  —  f  or 

(ir  -ne)  _ 
(Z  +  r) 

from  which  n  — — — — — -  revolutions-per-second. 

e  e  t 

From   this  it  will  be  seen  that  the  motor  will  develop  a  speed 


Current 

Current 

Current 

C.E.M.F. 

Speed, 

Revolu- 

8. 

thro' 

thro'  ar- 

in shunt 

Drop  in 

Drop  in 

of  arma- 

revolu- 

tions per 

$ 

lamps, 
amperes  *. 

mature, 
amperes 

amperes 

o-«i). 

shunt, 
volts. 

armature, 
volts. 

ture, 
volts. 

tions  per 
sec.,  n. 

lamp  per 
second. 

«!• 

I 

0.5 

0.05 

0.45 

0.045 

0.005 

0.040 

06.6 

0.66 

2 

I.O 

0.05 

o-95 

0.095 

0.005 

0.090 

i-5 

0-75 

4 

2.0 

0.05 

1-95 

0.195 

0.005 

0.190 

3-16 

0.79 

6 

3-° 

0.05 

2-95 

0.295 

0.005 

0.290 

4-83 

0.805 

8 

4.0 

0.05 

3-95 

0-395 

0.005 

0.390 

6-5 

0.813 

10 

5-0 

0.05 

4-95 

0495 

0.005 

0.490 

8.16 

0.816 

20 

IO.O 

0.05 

9-95 

0-995 

0.005 

0.990 

16.5 

0.825 

proportional  to  the  main  current  /,  if  the  frictional  torque  /, 
be   constant,   and   sufficiently   small  to   make  — small 

compared  with  — .    The  following  case  will  illustrate  this  result. 

Let  R  =  o.  i  ohm,  r  —  o.  i  ohm,  /  =  50  cm.-gms.,r  =  1,000 
em.-gms.-per-ampere,  e  —  0.06  volt  per  revolution  per  second. 
Then  n  =  1.6672  —  0.1667.  The  preceding  table  shows  the 
results  which  follow  for  various  currents  up  to  10  amperes, 
either  directly  from  the  formula  or  by  independent  reasoning. 

Such  a  motor  will  usually  operate  at  a  comparatively  high 
speed  at  full  load,  since  it  depends  upon  the  influence  of  its 
C.  E.  M.  F.  in  reducing  the  current  strength  through  the 
armature  to  that  required  in  order  just  to  balance  the  resisting 
torque  /. 

405.  If,  however,  a  load  torque  be  imposed  on  the  armature, 
proportional  to  the  speed,  represented  by  rl  —a  n,  then  our 
relation  becomes 

/   =  r  f  -|-  &  n 


316  ELECTRO-DYNAMIC  MACHINERY. 

i  r  —  n  e  r  ,  .   ,  /  r  t  —  f  (R  -f-  r) 

-   r  =  f  -4-  a  n,  from  which  n  = ; — -r^—, 

R  -\-  r  e  r  +  a  (R  +  r) 

revolutions-per-second. 

If,  for  example,  in  the  last  case,  the  motor  develops  a  re- 
tarding torque  of  6ocm.-gms.  per-revolution-per-second  (a  = 
60  cm.-gms.  or  60,000  cm. -dynes  approximately),  we  obtain 
either  from  the  formula,  or  by  direct  analysis,  the  following 
results  : 


CURRENT. 

TORQUE. 

DROP  IN  MOTOR 
ARMATURE. 

SPEED. 

- 

o 

j. 

ft 

2  • 

c    . 

Sa      1 

i 

Ml 

I 
M 

o 

1 

S 

"o 

-2 

o 

I 

fill 

•5  £ 

82        6 

u  ^            u 

*i    § 

s 

o 

s 

o 

2  fi 

•sa 

|| 

1-   0 
0   > 

to 

o 

% 
d 

V     ~" 

£  «      J3  rt 

3 

C    o- 

0 

H 

o  ^         -^ 

i 

tn 

o 
H 

1 

3 

0 

i 

W 

H 

fi 

o-S 

0.083 

0.417 

0.0417       50 

33 

83 

0.083 

0.0083  0.033 

0.0413 

0-55 

0-55 

i 

0.125 

o.87s 

0.0875 

so 

75 

125 

0.125 

0.0125  0.075 

0.0875 

1-25 

0.625 

2 

0.208 

1.792 

0.1792 

So 

158 

208 

0.208 

0.0208  0.158 

0.179 

2.633 

0.658 

3 

0.292 

2.708 

0.2708 

SO 

242 

292 

0.292 

0.0292  0.242 

0.271 

4-03 

0.667 

4 

0-375 

3-625 

0.3625 

50 

325 

375 

0-375 

0.0375  0.325 

0.3625 

5-42 

0.678 

S 

0-459 

4-541 

0.4541 

.SO 

409 

459 

0-459 

0.0459  0.409 

0-454 

6.82 

0.682 

10 

0.876 

9.124 

0.9124 

50 

826 

876 

0.876 

0.0876  1  0.826 

0.913 

18-97 

0.689 

406.  It  is,  therefore,  evident  that  a  motor  armature,  with 
constant  field  excitation,  can  develop  a  speed  closely  propor- 
tional to  the  pressure  at  its  terminals,  and,  therefore,  serve  as 
a  motor-meter,  if  the  retarding  torque  be  small  and  constant, 
or,  if  it  be  partly  small  and  constant,  and  partly  proportional 
to  the  speed. 


407.  One  of  the  most  important  recent  applications  of 
motors  is  their  distributed  application  to  machine  tools  in 
large  factories.  Instead  of  employing  long  lines  of  counter- 
shafting,  which  must  necessarily  be  constantly  driven  during 
working  hours,  a  separate  electric  motor  is  applied  directly  to 
each  machine,  so  that  each  machine  is  started  and  stopped 
according  to  its  own  requirements.  Moreover,  the  range  of 
regulation  of  speed,  which  is  obtainable  from  a  common  coun- 
tershafting,  is  necessarily  more  limited  in  degree  than  that 
which  can  be  effected  by  the  use  of  independent  motors. 


ME  TER-  MO  TORS.  3  I  ^ 

408.  By  the  use  of  individual  electric  motors,  not  only  is  each 
tool  capable  of  ^operation  at  its  best  speeds,  and  under  com- 
plete control,  but  also  the  friction  of  long  lines  of  counter- 
shafting  is  eliminated.  The  economy  is  greatest  where  the 
nature  of  the  work  in  the  machine  shop  is  such  that  the  average 
power  supplied  to  the  tools  is  much  less  than  the  maximum 
power,  or  the  ratio  of  average  to  maximum  power;  /".  ^.,  the 
load  factor  is  small,  since  the  motors,  when  completely  dis- 
connected from  a  circuit,  take  no  power,  whereas,  the 
countershafting  consumes,  practically,  the  same  amount  of 
power  friction,  whether  the  tools  be  active  or  idle. 


CHAPTER    XXX. 

MOTOR    DYNAMOS. 

409.  The  consideration  of  dynamos  and  motors  naturally 
leads  to  that  of  a  third   class  of  apparatus,  which  partakes  of 
the    nature  of  each;  namely,    motor- dynamos,    or,  as  they  are 
sometimes  called,  dyna-motors.     It  is  evident  that  if  a  motor 
be   rigidly   connected   to  a  dynamo,  either  by  a  belt  or  by  a 
coupling,  that  we  obtain  a  means  whereby  electric  power  can 
be  transformed  through  the  intermediary  of  mechanical  power. 
Thus,  the  motor  may  be  operated  from  a  high-tension  circuit, 
while  the  dynamo  .operates  a  low-tension  circuit,  Or  vice  versa  ; 
but,  neglecting  losses  taking  place  in   the  two  machines,  the 
amount  of  electric  energy   absorbed   and  delivered  in  the   re- 
spective circuits   will   be    the    same,    the    combination    being 
utilized  for  the  purpose  of  transforming  the  pressure  and  cur- 
rent strength.     For  this  reason  a  motor-dynamo  is  commonly 
called  a  rotary  transformer,  in  order  to  distinguish   it  from  an 
ordinary  alternating-current  transformer,  which  always  remains 
at  rest. 

410.  Instead   of  rigidly   connecting   together  two  separate 
machines;  /'.  <?.,  two  armatures  in  two  separate  fields,  the   plan 
has  been  adopted  of  placing  the  two  armatures  in  a  field  com- 
mon to  both;  as,  for  example,  by  placing  them  in  a  common 
field  of  double  length.      Or,  a  still  closer  union  can  be  effected 
by  winding  both  the  armature  and  motor  coils  on  a  common 
armature  core,  care  being  taken  to   insulate   the  two  sets  of 
windings  from  each  other.     Under  these  circumstances,  since 
the  intake  of  the  motor  winding  is  practically  equal  to  the  out- 
put of  the  dynamo  winding,  the  space  occupied  by  each  wind- 
ing will  be  practically  the  same,  so  that  where  both  are  asso- 
ciated on  a  common  core,  half  the  winding  space  is  appropriated 

318 


MOTOR  DYNAMOS.  319 

for  each.  The  result  will  be  that  if  the  motor  winding  or 
dynamo  winding  be  such  as  would  appertain  to,  say,  a  lo-KW 
capacity,  the  armature  in  which  the  two  are  associated  will  be 
a  machine  having,  approximately,  the  size  .and  weight  corre- 
sponding to  a  2O-KW  capacity.  There  is,  however,  an  econ- 


FIG.    23O. — STEP-UP    MOTOR    DYNAMO. 

omy  in  constructing  one  machine  of  double  capacity,  instead 
of  two  machines  of  single  capacity,  both  in  first  cost  and  in 
efficiency. 

411.  Rotary  transformers,  like  all  transformers,  may  be  either 
of  the  step-up  or  step-down  type.  Fig.  230  represents  a  step- 
up  rotary  transformer  of  I.5-KW  capacity,  transforming  from 
120  volts  and  12.5  amperes,  to  5,000  volts  and  0.3  ampere. 
The  motor  winding  of  the  armature  is  connected  with  the  com- 
mutator on  the  left,  while  the  generator  winding  of  the  arma- 
ture is  connected  with  the  commutator  on  the  right.  The 
magnet  coils  are  excited  from  the  low-tension  mains.  The 
two  armature  windings,  in  such  cases,  may  be  either  placed  one 
below  the  other,  or  they  may  be  interspersed.  The  left  hand 


320  ELECTRO-DYNAMIC  MACHINERY. 

brushes  receive  the  i2o-volt  pressure,  and  the  right  hand 
brushes  deliver  the  5,ooo-volt-pressure.  The  function  of  such 
a  machine  is  to  test  high-tension  insulation  under  practical 
conditions  of  pressure. 

412.   Fig.  231  represents  a  step-down  rotary  transformer  for 
transforming  from  500  to  120  volts.     In  this  case  the  smaller 


FIG.    231. — STEP-DOWN    DYNAMO. 

brushes  are  connected  to  the  5oo-volt  mains,  as  is  also  the  field 
winding,  and  the  lower  pressure  is  delivered  at  the  heavy 
brushes. 

413.  It  is  important  to  observe  that  in  a  motor  dynamo  of 
the  preceding  types  there  is  no  appreciable  armature  reaction. 
The  reason  for  this  is  as  follows:  The  M.  M.  F.  of  the  motor 
armature  winding  is,  as  we  know,  opposite  in  direction  of  that 
of  the  generator  winding;  and,  since  these  M.  M.  Fs.  are 


MO  TOR  D  YNAMOS.  32 1 

nearly  equal,  and  are  produced  on  the  same  core,  they  will 
nearly  neutralize  each  other.  Consequently,  the  brushes  of 
such  a  machine  never  require  to  be  shifted  during  variations 
of  load,  and  the  commutators  are  characterized  by  quiet  and 
sparkless  operation. 

414.  Under  ordinary  circumstances  it  is  necessary  to  excite 
the  field  magnet  of  a  motor  dynamo  from  the  primary  circuit, 
since,  otherwise,  the  motor  side  could  not  be  operated.     It  is 
often  possible,  however,  to  place  a  series  winding  on  the  motor 
side,  and  a  shunt  winding  on  the  secondary  or  dynamo  side. 
Thus,  if  it  be   required   to  transform  from  1,000  to  50  volts,  a 
shunt-field  winding  for  1,000  volts  would  be  more  expensive 
than  one  for  50  volts.     In  such  a  case  it  becomes  possible  to 
excite  the  fields  by  a  few  turns  of  series  winding,  carefully  in- 
sulated, in  the  primary  circuit,  in  order  to  start  the  machine 
from  rest,  and  to  supply  the  balance  of  the  field  excitation  by 
a  shunt  winding  on  the  secondary  side,  which  commences  to 
be  actuated  as  soon  as  the  motor  starts. 

415.  It  will  be  evident  that  any  variation  in  the  strength  of 
the  field  magnets,  whether  these  be  shunt-  or  series-wound,  will 
not  vary  the  ratio  of  transformation;  for,  although  by  varying 
the  field  excitation   the  motor  can  be  made  to  change  speed, 
yet  this  speed  will  not  produce  any  appreciable  effect  upon  the 
generated  E.  M.  F.,  since  the  field  is  proportionally  weakened. 
In  other  words,  the  C.    E.   M.   F.    in   the  motor  being  always 
equal  to  the  E.  M.  F.  at  the  brushes,  after  deducting  the  drop 
in  the  armature,   the  generated  E.    M.    F.,    which    is   always 
some  fixed  fraction  of  the  motor  C.  E.  M.  F.,  must  be  constant 
within  the  same  limits.     If  the  number  of  turns  in  the  motor 
winding,  counted  once  all  round  the  armature,  be  «/„„  and  the 
number  of  turns  in  the  generator  winding,  counted  in  the  same 

MTfJ 

manner,  be  wg^  then  the  ratio  —?-  is  called  the  ratio  of  transfor- 
mation. If,  then,  the  primary  E.  M.  F.  be  El  volts,  the  primary 
current  7l  amperes,  and  the  resistance  in  the  primary  winding 
rt  ohms,  while  the  corresponding  quantities  in  the  secondary 
circuit  are  E^  72,  and  ra,  respectively,  the  C.  E.  M.  F.  in  the 
primary  winding  will  be  n  ^  =  £,  —  7,  r^  where  »,  is  the  speed 


3-2  ELECTRO-DYNAMIC  MACHINERY. 

of  revolution  in  turns-per-second,  and  <?,,  the  dynamo  power,  or 
3>wm  x  io~8.     The  generated  secondary  E.  M.  F.  will  be  ;/  3>wf 

IV 

X    io-8  volts  =  (£t  —  II  rt)  —*. 

WHI 

The  pressure  at  the  secondary  terminals  will  be  further  re- 
duced by  the  drop  in  the  secondary  winding;  or 

E*  =  (A  ~  A  >\)  —  ~  ^  >V 

l'   Wm 

Tf  the  weight  of  copper  in  the  two  windings  is  equal,  72  ;-2,  will 

T  V  *i$) 
practically  be  equal  to  —  -  —  !  —  -,  so  that 


Wm 

The  machine,  therefore,  acts  as  though  it  were  a  dynamo  of 

E.  M.  F.  !-2L  E    with  an  internal  resistance  of  zr  ,  or  twice  that 
wm 

of  the  secondary  winding. 

416.  In  all  motor  dynamos,  having  a  field  magnet  common 
to  both  armatures,  the  ratio  of  transformation,  neglecting  ar- 
mature drop,  is  constant,  no  matter  how  the  field  excitation  is 
varied.     Motor-generators  are  often    employed  for  raising  or 
lowering   the    pressure  of  continuous-current  circuits.     Thus 
electroplating  E.  M.  Fs.  of,  say  6  volts,  are  obtainable  in  this 
manner  from  circuits  of  no,  220  or  500  volts  pressure.     Simi- 
larly, pressure  of  150  volts  are  obtainable  from  a  few  storage 
batteries  by  such  apparatus. 

417.  In  central  stations  for  low-pressure  distribution,  say  at 
220  volts,  by  a  three-wire  system,  some  of  the  feeders  have  to 
be  maintained  at  a  higher  pressure  than  others,  in  order  that 
all  the  feeding  points,  or  points  of  connection  between  feeders 
and   the  mains,  should   have  the  same  pressure.     This  is  ac- 
complished   either  by  employing   separate  dynamos,  operated 
at  slightly  different  pressures,  or  by  introducing  at  the  central 
station  motor-dynamos  having  their  dynamos  in  circuit  with  the 
feeders.     Such  motor-dynamos  are   frequently  called  boosters. 
The  motor-dynamo  for  this  purpose  requires  that  means  should 
be  provided  for  regulating  the  E.  M.  F.  which   is  to  be  added 
to  the  feeder  circuit.     This  can  only  be  done  by  employing 
separate  field  magnets  for  the  motor  and  generator  armatures. 


OF  THE 

NIVERSITY) 

N.  OF  .        jr 

MOTOR   DYNAMOS.  323 

Fig.  232  represents  a  practical  form  of  booster  employed  in 
a  three-wire  central  station.  The  middle  machine  is  a  motor 
operated  at  central-station  pressure  of,  perhaps,  250  volts;  the 
others  are  generators,  having  their  armatures  coupled  to  the 
same  shaft  as  that  of  the  motor  armature.  One  dynamo  is 


FIG.    232. — BOOSTER    IN    THREE-WIRE    CENTRAL    STATION. 

connected  in  circuit  with  the  positive  conductor  of  the  feeder 
whose  pressure  is  to  be  raised,  and  the  other  is  connected  in 
the  circuit  of  the  negative  conductor.  Since  these  feeders 
carry  heavy  currents  and  require  to  be  of  very  low  resistance, 
the  necessity  for  the  massive  copper  brushes  and  connections 
of  the  dynamos  will  be  evident.  The  amount  of  E.  M.  F.  which 
will  be  generated  in  these  armatures  will  be  determined  by  the 
excitation  of  their  field  magnets. 


THE    END. 


INDEX. 


Active  Conductor,  Magnetic  Flux 

of,  37 
Aero-Ferric     Magnetic    Circuits, 

68-73 

Air-Gap,  Magnetic,  57 
Air-Path,  Alternative  Magnetic,  42 

—  Aligned  M.  M.  F.,  56 
Alternating-Current  Dynamos,  17 
Alternative  Magnetic  Air-Path,  52 
Alternators,  17 

—  Multiphase,  25 

—  Uniphase,  26 
Ampere,  Definition  of,  49 
Ampere-Hour  Meter,  313 
Ampere-Turn,  Definition  of,  40 
Anomalous  Magnet,  47 
Arc-Light  Dynamos,  26 
Armature,  Back  Magnetization  of, 

1 86 

—  Cores,  Cross-Sections  of,  126 
— ,  Core  Discs  for,  152 

—  Core,  Lamination  of,  105 
— ,  Cylinder  or  Drum,  23 

—  Disc,  23 

—  Double  Winding  of,  190 

—  Gramme-Ring,  23 

—  PR,  Loss  in,  200 

—  Iron-Clad,  Definition  of,  24 

—  Journal  Bearings,  159-163 

—  of  Machine,  9 

—  Neutral  Line  of,  184 

—  Pole,  110-116 

—  Radial,  no 

—  Reaction  and  Sparking  at  Com- 
mutators, 179-198 

—  Ring,  23 

— ,  Smooth-Core,  23,  152 
Definition  of,  24 

—  Toothed-Core,  152 
,  Definition  of,  24 

1  23 

—  Turns,  Effect  of,  on  E.  M.  F.,  3 

—  Winding,  Closed-Coil,  no 
,  Disc,  230 

,  Dissymmetry  of,  125 

,  Inter-Connected,  145 

Space,  275 

—  Wire,  Effective  Length  of,  246 


Armatures,  Closed-Coil,  217 

— ,  Gramme-R.ing,  117-127 

— ,  Lap  Winding  for,  155 

— ,  Open-Coil,  217 

— ,  Wave- Winding  for,  155 

Attractions  and  Repulsions,  Laws 
of  Magnetic,  33 

Automatic  Regulation  of  Dyna- 
mos, 218 

Average  Efficiency  of  Motor,  279 

Back  Magnetization  of  Armature, 
1 86 

Balancing  Coil  of  Armature,  194 

Bar,  Equalizing,  224 

Bars,  Bus,  224 

— ,  Omnibus,  224 

Bearings,  Self-Oiling,  161 

Belt-Driven  Dynamos,  18,  135 

Bipolar  Dynamo,  16 

Boosters,  322,  323 

Box,  Field-Regulating,  for  Dy- 
namo, 14 

Brush,  Dynamo,  124 

Brushes,  Forward  Lead  of,  217 

— ,  Lead  of,  185 

—  of  Dynamo,  9 

—  of  Motor,  Lag  of,  303 
Bus  Bars,  224 

Calculation  of  Gramme-Ring  Dy- 
namo Windings,  128-134 

Capability,  Electric,  of  Dynamo, 
126 

— ,  Electric,  of  Dynamo-Electric 
Machine,  4 

Car  Motor,  277 

Characteristic  Curve  of  Dynamos, 
210 

—  External,  of  Series- Wound  Dy- 
namo, 210 

—  Internal,  of  Series- Wound  Dy- 
namo, 210 

—  of  Shunt- Wound  Dynamo,  212 
Circuit,  Magnetic,  48 

—  Return,  for  Track  Feeders,  226 
Circuits,  Ferric-Magnetic,  55-67 
— ,  Magnetic,  Non-Ferric,  48-54 


325 


326 


INDEX. 


Circuit,  Transmission,  Definition 
of,  i 

Circular  Distribution  of  Magnetic 
Flux  Around  Conductor,  37 

— ,  Magnetic  Flux,  Assumed  Di- 
rection of,  39 

Closed  Circular  Solenoid,  50 

—  Coil  Armature  Winding,  no 

Armatures,  217 

Coefficient,  Hysteretic,  174 

Coil,  Balancing,  of  Armature,  194 

— ,  Inductance,  301 

— ,  —  of,  181 

— ,  Starting,  301 

Combinations  of  Dynamos  in  Se- 
ries or  in  Parallel,  220-227 

Commercial  Efficiency  of  Dyna- 
mo, 5 

of  Dynamos,  Circumstances 

Affecting,  7 

of  Motor,  268 

Commutation,  Definition  of,  180 

— ,  Diameter  of,  180 

— ,  Quiet,  Circumstances  Favor- 
ing, 187 

— ,  Sparkless,  Circumstances  Fa- 
voring, 1 86 

Commutator,  Circumstances  Fa- 
voring Sparking  at,  186 

— ,  Forms  of,  123 

—  of  Dynamo,  9 

Commutatorless,  Continuous-Cur- 
rent Dynamo,  Disc  Type  of,  236 

Dynamos,  234 

Generators,  234-240 

Commutators,   Sparking  at,    179- 

198 
Compound  Magnets,  105 

—  Winding  of  Dynamos,  208 
Compound- Wound  Dynamos,  14 

,  Uses  for,  209- 

Conductor,  Active,  Magnetic  Flux 

of,  37 

Consequent  Poles  of  Dynamo,  22 
Constant-Current  Dynamos,  10 
Constant-Potential  Dynamos,  10 
Constants,  Reluctivity,  Table  of, 

65 

Continuous-Current  Commutator- 
less  Dynamos,  28,  234 

,  Cylinder  Type  of,  236 

Dynamo,  20 

Generators,  234-240 

Generator,  Limitations  to 

Output  of,  203 

Convention  as  to  Direction  of  Cir- 
cular Magnetic  Flux,  39 

Converging  Magnetic  Flux,  35 

Core  Discs  for  Armatures,  152 


Core,  Effect  of  Lamination  on 
Eddy  Currents,  166 

Coulomb  Meter,  313 

Counter  Electro-Dynamic  Force, 
256 

Cross  Magnetization,  183 

Currents,  Eddy,  164-171 

— ,  Eddy,  Definition  of,  164 

— ,  — ,  Effect  of  Lamination  of 
Core  on,  166 

— ,  — ,  Origin  of,  165 

Curves,  Characteristic  of  Dyna- 
mos, 210 

—  of  Reluctivity  in   Relation   to 
Flux  Density,  66 

Cutting  Process  vs.  Enclosing  of 

Magnetic  Flux,  82 
Cycles  of  Magnetization,  174 
Cylinder  or  Drum  Armature,  23 

—  Type  of  Commutatorless  Con- 
tinuous-Current Dynamos,  236 

Decipolar  Dynamos,  17 

Density,  Flux,  34 

— ,  Prime  Flux,  54 

Devices,     Receptive,      Definition 

of,  i 

Diameter  of  Commutation,  180 
Diffusion,  Magnetic,  52,  53 
Diphase  Dynamo,  27 
Direct-Driven  Dynamos,  135 
Disc  Armature,  23 

—  Armature  Winding,  230 

—  Armatures  and  Single    Field- 
coil  Machines,  228-233 

— ,  Faraday's,  234 

—  Type  of  Commutatorless   Con- 
tinuous-Current Dynamos,  236 

Dissymmetry,  Magnetic,  124 

—  of  Armature  Winding,  125 
Distribution  of  Magnetic  Field,  41 

-47 

—  of  Magnetic  Flux,  31 

—  of  Magnetic  Flux  of  Conductor, 

Diverging  Magnetic  Flux,  35 
Double  Circuit,  Bipolar  Dynamo, 

16 

Double  Winding  of  Armature,  190 
Drum  Armatures,  152 

—  or  Cylinder  Armatures,  23 
Dynamo  Armatures,    Electro-Dy- 
namic Induction  in,  90-102 

— ,  Bipolar,  16 

—  Brush,  124 

—  Brushes  of,  9 

— ,  Commercial  Efficiency  of,  5 

—  Commutator,  9 

— ,  Consequent  Poles  of,  22 


INDEX. 


327 


Dynamo,  Continuous-Current,  20 
— ,  Biphase,  27 

— ,  Double-Circuit,  Bipolar,  16 
— ,  Electric  Capability  of,  126 
— ,  —  Efficiency  of,  5 
Dynamo-Electric  Generator,  2 

Machine,  Electric  Capability 

of,  5 
Dynamo  Field-Regulating  Box,  14 

—  Intake,  5 

—  Load  of,  15 

—  Magneto-Electric,  n 

—  Output  of,  5 

—  Plating,  26 

Dynamo-Power  of  Motor,  266 
Dynamo  Relation  between  Output 

and  Resistance,  6 

— ,  Self-Excited,  12 

— ,  — ,  Compound-Wound,  13 

— ,  Separately  Excited,  12 

— ,  Single-Circuit,  Bipolar,  16 

— ,  Telegraphic,  26 

Dynamos,  Alternating-Current,  17 

— ,  Arc-Light,  26 

— ,  Automatic   Regulation  of,  218 

— ,  Belt-Driven,  18 

— .  Characteristic  Curves  of,  210 

— ,  Circumstances  Influencing 
Electric  and  Commercial  Effi- 
ciency of,  7 

— ,  Combination  of,  in  Series  or 
Parallel,  220-227 

— ,  Commutatorless  Continuous- 
Current,  28,  234 

— ,  Compound- Wound,  14 

— ,  — ,  Uses  for,  209 

— ,  Constant-Current,  10 

— ,  Constant-Potential,  10 

— ,  Decipolar,  17 

— ,  Direct-Driven,  135 

— ,  Heating  of,  199-205 

— ,  Incandescent  Light,  26 

— ,  Inductor,  25 

— ,  Multipolar,  16 

— ,  Multipolar,  Gramme-Ring,  135 

-151 

— ,  Octopolar,  17 
— ,  Over-Compounded,  209 
— ,  Quadripolar,  17 
— ,  Regulation  of,  206-219 
— ,  Self -Excited,  Series- Wound,  13 
— ,  Series-Wound,  Uses  for,  209 
— ,  Sextipolar,  17 
— ,  Shunt-Wound,  Uses  for,  209 
— ,  Simple  Magnetic  Circuits,  22 
— ,  Single-Field-Coil,    Multipolar, 

28 

— ,  Single-Phase,  27 
— ,  Three-Phase,  27 


Dynamos,  Triphase,  27 
— ,  Two-Phase,  27 
— ,  Unipolar,  28 
Dynamotors,  317 
Dyne,  Definition  of ,'69 

E.  M.  P.,  Effect  of  Number  of 
Armature  Turns  on,  3 

— ,  Effect  of  Speed  of  Revolution 
on,  3 

— ,  Induced  by  Magneto  Genera- 
tors, 103-109 

— ,  Induced  in  Loop,  Rule  for 
Direction  of,  94 

— ,  of  Electro-Dynamic  Induction, 
Value  of ,  75-82 

— ,  of  Self-induction,  181 

— ,  of  Self-induction,  Circum- 
stances Affecting  Value  of,  182 

— ,  Produced  by  Cutting  Earth's 
Flux,  90 

Earth's  Flux,  E.  M.  F.  Produced 
by  Cutting,  90 

Eddy  Currents,  164-171 

,  Definition  of,  164 

,  Effect  of  Lamination  of 

Core  on,  166 

,  Formation  of,  in  Pole-pieces, 

169 

,  Origin  of,  165 

Edges,  Leading,  of  Pole-pieces,  184 

Efficiency,  Average,  of  Motor,  270 

— ,  Full  Load  of  Motor,  270 

—  of  Motors,  268-279 

Electric  Capability  of  Dynamo, 
126 

—  —  of    Dynamo-Electric    Ma- 
chine, 5 

—  Efficiency  of  Dynamos,  Circum- 
stances Affecting,  7 

—  Flux,  Unit  of,  49 
Electro-Dynamic  Force,  241-249 

—  Induction,  75-82 

in  Dynamo  Armature,  90-102 

,  Laws  of,  74-89 

—  Machinery,  i 

—  Machinery,  Classification  of,  i 
Enameled  Rheostats,  216 
Entrefer,  105 

Equalizing  Bar,  224 
Ether,  Assumed  Properties  of,  29 
Ether  Path  of  Reluctivity,  60 
External  Characteristic  of  Series- 
Wound  Dynamo,  210 

Factor,  Leakage,  132 

— ,  Load,  317 

Faraday's  Disc,  234 

Feeders  for  Return  Track,  226 


328 


INDEX. 


Eeedin  3  Points,  322 

Ferric  Magnetic  Circuits,  55-67  : 

—  Path  of  Metallic    Reluctivity, 
60 

Field  Magnet  of  Machine,  9 
— ,  Magnetic,  32 

—  Magnets,  Is  R  Losses  in,  199 

—  Poles,  Eddy-Current  Losses  in, 
200 

—  Regulating  Box  for  Dynamo,  14 

—  Rheostats,  215 

Fleming's  Hand  Rule  for  Dyna- 
mos, 74 
Motors,  243 

Flux,  Circular  Magnetic,  Conven- 
tion as  to  Direction  of,  39 

— ,  Converging  Magnetic,  35 

—  Density,  34 

— ,  Diverging  Magnetic,  35 
— ,  Magnetic,  Unit  of,  49 

—  Density,  Prime,  54 
— ,  Prime,  56 

— ,  Magnetic,  29 

— ,  — ,  Distribution  of,  31 

— ,  — ,  Irregular,  35 

— ,  — ,  Variations  of,  33 

—  Paths,  Magnetic,  2 
Following  Edges  of  Pole-Pieces, 

184 
Force,  M.  M.,  Induced,  56 

—  Electro-Dynamic,  241-249 

—  Lines  of  Magnetic,  34 

—  Magnetic,  Tubes,  35 

—  Magnetizing,  53 

—  Magnetomotive,  31 

—  — ,  Prime,  56 

Forces,    Electromotive,    Methods 

for  Increasing,  3 
French  Measures,  Table  of,  8 
Friction   Losses  in  Bearings  and 

Brushes,  201 
— ,  Magnetic,  174 
Full-Load  Efficiency  of  Motor,  270 

Gap,  Magnetic  Air,  57 
Gauss,  Definition  of,  35 
Generator     Armature,     Limiting 

Temperature  of,  203 
— ,  Dynamo-Electric,  2 
Generators,  Commutatorless  Con- 

tinuous-Current,«234~24o 
— ,  Definition  of,  i 
Gilbert,  Definition  of,  40 
Gramme-Ring  Armature,  23 

—  Armatures,  117-127 

—  Dynamos,  Multipolar,  135-151 

Hand  Rule,  Fleming's,  for  Dyna* 
mos,  74 


Heating  of  Dynamos,  199-205 
Hysteretic  Activity,  Table  of,  175 

—  Losses  in  Armature  and  Field 
Poles,  200 

—  Loss,  174 

—  Coefficient,  174 
Hysteresis,  Magnetic,  172-178 
— ,  — ,  Definition  of,  172 

Incandescent  Light  Dynamos,  26 
Individual  Electric  Motors,  317 
Idle  Wire  on  Armature,  100 
Inductance  Coil,  301 

—  of  Coil,  181 

Induction,  Electro-Dynamic,  75-82 
— ,  — ,  Laws  of,  74-89 

—  in  Dynamo  Armature,  90-102 
— ,  Self,  E.  M.  F.  of,  181 
Inductor  Dynamos,  25 

Intake  of  Dynamo,  Definition  of,  5 
Inter-Connected  Armature  Wind- 
ing, 145 

Internal  Characteristics  of  Series- 
Wound  Dynamo,  210 
Iron-Clad  Armature,  24 
Irregular  Magnetic  Flux,  35 

Joint  Reluctivity,  60 
Journal  Bearings  for  Armatures, 
159-163 

Lag  of  Motor  Brushes,  303 
Lamination    of    Armature    Core, 

105 

Lamp,  Pilot,  Definition  of,  12 
Lap  Winding  for  Armatures,  155 
Laws  of  Electro-Dynamic  Induc- 
tion, 74-89 

—  —  Magnetic  Attractions  and 
Repulsions,  33 

Lead,  Forward,  of  Dynamo 
Brushes,  217 

—  of  Brushes,  195 

Leading  Edges  of  Pole-pieces,  184 

—  Pole  of  Motor,  303 
Leakage  Factor,  132 
— ,  Magnetic,  52,  53 

Length,  Effective,  of  Armature 
Wire,  246 

Limitation  to  Output  of  Continu- 
ous-Current Generator,  203 

Limiting  Temperature  of  Genera- 
tor Armature,  203 

Line,  Neutral,  of  Armature,  194 

Lines  of  Magnetic  Force,  34 

— ,  Stream,  30 

Load  Factor,  317 

—  of  Dynamo,  15 
Locomotors,  273 


INDEX. 


329 


Loss  by  Eddy  Currents  in  Arma- 
ture and  Field  Poles,  200 

— ,  Hysteretic,  174 

— ,  — ,  in  Armature  and  Field 
Poles,  200 

Losses,  I2  R,  in  Field  Magnets,  199 

—  in  Armature,  I2  R,  200 

—  Produced  by  Air-Churning,  201 
Friction  in  Bearings  and 

Brushes,  201 

M  M.  F.,  Aligned,  56 

—  Induced,  56 

—  Methods  of  Producing,  38 

—  Prime,  56 

—  Structural,  56 

—  Unit  of,  40 
Machine,  Armature  of,  9 

—  Circumstances        Influencing 
Electric     Efficiency    of    Dyna- 
mos, 7 

— ,  Field  Magnet  of,  9 
— ,  Magnetic  Flux  Produced  by,  9 
Machinery,  Electro-Dynamic,  i 
— ,  — ,  Classification  of,  i 
Machines,   Disc     Armature    and 

Single  Field-Coil,  228-233 
Magnet,  Anomalous,  47 
— ,  Mechanical   Analogue  of,  30 
— ,  North-Seeking  Pole  of,  29 
Magnets,  Compound,  105 
— ,  Molecular,  56 
Magnetic  Air-Gap,  57 

—  Air  Path,  Alternative,  52 

—  Attractions     and     Repulsions, 
Laws  of ,  33 

—  Circuit,  48 

—  Circuit,  Application  of    Ohm's 
Law  to,  49 

—  Circuits,  Aero-Ferric,  68-73 

—  Diffusion,  52,  53 

—  Field,  32 

—  Dissymmetry,  124 

—  Field,  Distribution  of,  41-47 

,  Method  of  Mapping,  32 

,  Negatives  of,  32 

•,  Photographic  Positives  of,  32 

—  Flux,  29 

,  Converging,  35 

,  Cutting  Process,  Enclos- 
ing, 82 

Density,  34 

,  Diverging,  35 

,  Effect  of,  on  C.  E.  M.  F.,  58 

,  Irregular,  35 

of  Dynamo,  9 

,  Uniform,  35 

,  Unit  of,  49 

,  Unit  of  Intensity  of,  35 


Magnetic  Flux,  Variations  of,  33 

—  Force,  Tubes  of,  35 

—  Friction,  174 

—  Hysteresis,  172-178 
,  Definition  of,  172 

—  Intensity,  34 

—  Leakage,  52,  53 

—  Permeability,  55 
,  Definition  of,  3 

—  Potential,  Fall  of,  53 

—  Reluctance,  48 
Magnetism,  Definition  of,  29 
— ,  Molecular,  56 

— ,  Residual,  55,  173 

— ,  Streaming-Ether  Theory  of, 
29 

Magnetization,  Back,  of  Arma- 
ture, 1 86 

— ,  Cross,  183 

— ,  Cycles  of,  174 

Magnetizing  Force,  53 

in  Relation  to  Reluctivity, 

59 

Magneto-Electric  Dynamo,  n 
Magneto    Generators,   E.    M.    F. 

Induced  by,  103-109 
Magnetomotive  Force,  31 
Mapping  of  Magnetic  Field,  32 
Mechanical    Analogue    of     Mag- 
net, 30 

Meter  Motors,  309-317 
Methods  for  Suppressing  Spark- 
ing, 189 
Molecular  Magnetism,  56 

—  Magnets,  56 

Motor,  Average  Efficiency  of,  270 
— ,  Commercial  Efficiency  of,  268 
— ,  Dynamo-Power  of,  264 

—  Dynamos,  318-323 
— ,  Definition  of,  318 

— ,  Full-Load  Efficiency  of,  270 
— ,  Leading  Pole  of,  303 

—  Torque,  251-267 

— ,  Trailing  Pole  of,  303 

Motors,  Efficiency  of,  268-279 

— ,  Fleming's   Hand  Rule  for,  243 

—  for  Street  Car,  277 

— ,  Individual  Electric,  217 

— ,  Regulation  of,  280-296 

— ,  Slow  Speed,  271 

— ,  Starting  and  Reversing  of,  291 

-308 

— ,  Stationary,  273 
— ,  Traveling,  273 
Multiphase  Alternators,  26 
Multipolar  Dynamos,  16 
,  Single-Field-Coil,  28 

—  Gramme-Ring   Dynamos,    135- 
151 


33° 


INDEX. 


Negatives  of  Magnetic  Fields,  32 
Neutral  Line  of  Armature,  184 

—  Wire  of  Three-Wire  System,  221 
Non-Ferric      Magnetic     Circuits, 

48-54 
North-Seeking  Pole  of  Magnet,  29 

Octopolar  Dynamos,  17 

Oersted,  Definition  of,  49 

Ohm,  Definition  of,  49 

Ohm's  Law,  49 

Applied  to  Magnetic  Cir- 
cuit, 49 

Oilers,  Sight-Feeding,  160 

Omnibus  Bars,  224 

Open-Coil  Armatures,  217 

Over-Compounded  Dynamos,  209 

Output  and  Dimensions  of  Dyna- 
mos, Relation  Between,  136 

—  of  Dynamo,  Definition  of,  5 
,  Relation   Between  and  Re- 
sistance, 6 

Permeability,  Magnetic,  55 
— ,  — ,  Definition  of,  3 
Photographic  Positives    of   Mag- 
netic Fields,  32 
Pilot  Lamp,  Definition  of,  12 
Plating  Dynamo,  26 
Points,  Feeding,  322 
Pole  Armature,  25 

—  Armatures,  110-116 

— ,  Leading,  of  Motor,  303 

— ,  North-Seeking  of  Magnet,  29 

— ,  South-Seeking,  29 

— ,  Trailing,  of  Motor,  303 

Pole-Pieces,  Following  Edges  of, 

184 
— ,  Formation   of  Eddy  Currents 

in,  169 

— ,  Leading  Edges  of,  184 
Poles,  Consequent,  of  Dynamo,  22 
Potential,  Magnetic,  Fall  of,  53 
Prime  Flux,  56 

—  Flux  Density,  54 

—  M.  M.  F.,56 

Properties,  Assumed,  of  Ether,  29 

Buadripolar  Dynamos,  17 
uiet  Commutation,  Circumstan- 
ces Favoring,  187 

Radial  Armature,  no 
Ratio  of  Transformation,  321 
Receptive  Devices,  Definition  of,  i 
Regulation  of  Dynamos,  206-219 

—  of  Motors,  280-296 
Reluctance,  48 

— ,  Magnetic,  48 


Reluctance,  Unit  of,  49 

Reluctivity,  48 

— ,  Constants,  Table  of,  65 

—  Curves    in   Relation   to    Flux 
Density,  66 

— ,  Ether  Path  of,  60 

—  in     Relation     to    Magnetizing 
Force,  59 

— ,  Joint,  60 

— ,  Metallic,  Ferric  Path  of,  60 

Residual  Magnetism,  55,  173 

Resistivity,  48 

Return  Track  Feeders,  226 

Reversing  and  Starting  of  Motors,. 

291-308 

Rheostats,  Enameled,  216 
— ,  Field,  215 
— ,  Starting,  298 
Ring  Armature,  23 
Ring  Armatures,    Gramme,    117- 

127 

Rotary  Transformers,  318 
Rule,  Fleming  Hand,  for  Motors,. 

243 

—  for  Direction  of  E.  M.   F.  In- 
duced in  Loop,  94 

Self-Excited  Compound- Wound 
Dynamo,  13 

—  Dynamo,  12 

—  Series-Wound  Dynamos,  13 
Self-Induction,  E.  M.  F.,  of,  181 

—  E.  M.  F.,  of,  Circumstances  Af- 
fecting Value  of,  182 

Self-Oiling  Bearings,  161 
Separately-Excited  Dynamo,  12 
Series  or  Parallel  Combinations  of 
Dynamos,  220-227. 

—  Winding  of  Dynamos,  206 
Series- Wound  Dynamo,  External 

Characteristic  of,  210 

—  Dynamo,  Internal     Character- 
istic of,  210 

Sextipolar  Dynamo,  17 
Shunt  Winding  of  Dynamos,  207 
Shunt-Wound    Dynamo,  Charac- 
teristic of,  212 

—  Dynamos,  Uses  for,  209 
Sight-Feeding  Oilers,  160 
Simple    Magnetic    Circuit   Dyna- 
mos, 22 

Single-Circuit  Bipolar  Dynamo, 
16 

Single  Field-Coil  Multipolar  Dy- 
namos, 28 

Single-Phase  Dynamos,  27 

Slow  Speed  Motor,  271 

Smooth-Core  Armature,  23 

—  Armatures,  152 


INDEX. 


331 


Smooth-core  Armature,  Definition 

of,  24 

Solenoid,  Closed  Circular,  50 
Sources,  Electromotive,  2 
South-Seeking  Pole,  29 
Space  for  Armature  Winding,  275 
Sparking  and  Armature  Reaction, 

179-198 

—  at  Commutator,  Circumstances 
Favoring,  186 

— ,  Definition  of,  iSo 

— ,  Methods  for  Suppressing,  189 

Sparkless  Commutation,  Circum- 
stances Favoring,  186 

Specific  Resistance,  48 

Speed  of  Revolution,  Effect  of,  on 
E.M.F.,3 

Starting  and  Reversing  of  Motors, 
291-308 

—  Coil,  301 

—  Rheostats,  298 
Stationary  Motors,  273 
Step-Down  Transformers,  319 
Step-Up  Transformers,  319 
Stream  Lines,  30 

Streaming-Ether  Theory  of  Mag- 
netism, 29 

Structural  M.  M.  F.,  56 
System,  Three-Wire,  221 

Table  of  French  Measures,  8 

—  of  Hysteretic  Activity,  175 

—  of  Reluctivity  Constants,  65 
Telegraphic  Dynamo,  26 
Thermal  Losses,  204 
Three-Phase  Dynamos,  27 
Three  Phasers,  27 

Three- Wire  System,  221 

,  Neutral  Wire  of,  221 

Toothed-Core  Armature,  23 
,  Definition  of,  24 

—  Armatures,  152 
Torque,  Definition  of,  251 
— ,  Motor,  251-267 
Transformation,  Ratio  of,  321 
Transformers,  Rotary,  318 
— ,  Step-Down,  319    * 

— ,  Step-Up,  319 

Transmission  Circuits,  Definition 
of,  i 


Travelling  Motors,  273 
Triphase  Dynamos,  27 
Triphasers,  27 

Tubes  of  Magnetic  Force,  35 
Turns,   Armature,    Effect   of,  on 

E.  M.  F.,  3 

Two-Phase  Dynamos,  27 
Two  Phasers,  27 

Uniform  Magnetic  Flux,  35 
Uniphase  Alternators,  26 
Unipolar  Dynamos,  28,  234 
Unit  of  Electric  Flux,  49 

Force,  in  C.  G.  S.  System,  68 

M.  M.  F.,  40 

Magnetic  Flux,  49 

Intensity,  35 

Reluctance,  49 


Variations  of  Magnetic  Flux,  33 

Volt,  Definition  of,  49 

Voltaic  Analogue   of  Aero-Ferric 

Circuit,  69 
Simple  Ferric  Circuit,  69 

—  Circuit,  Magnetic  Analogue  of, 
53 

Wattmeter,  313 

Wave    Winding  for    Armatures, 

155 

Weber,  Definition  of,  49 
Winding,  Closed-Coil    Armature, 

no 

— ,  Compound,  of  Dynamos,  208 
— ,  Disc  Armature,  230 

—  for  Armature,  Inter-Connected, 

145 

Armatures,  Lap,  155 

Armature,  Wave,  155 

—  of  Gramme-Ring  Dynamo,  Cal- 
culations of,  128-134 

— ,  Shunt,  of  Dynamos,  207 
— ,  Space,  for  Armature,  275 
Wire,  Armature,  Effective  Length 

of,  246 

— ,  Idle,  on  Armature,  100 
— ,  Neutral,  of  Three-wire  System, 

221 


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